Yes, the apostles were eye witnesses to the fact that Jesus had been resurrected. The arguments presented here against this stated requirement are without merit.
Being an eyewitness to Jesus' resurrection meant that they had seen Jesus after he rose from the grave. While there were many disciples, Jesus selected the original twelve specifically, and named them "apostles" as is stated in Luke 6:13.
"13 And when it was day, he called unto him his disciples: and of them he chose twelve, whom also he named apostles; 14 Simon, (whom he also named Peter,) and Andrew his brother, James and John, Philip and Bartholomew, 15 Matthew and Thomas, James the son of Alphaeus, and Simon called Zelotes,
16 And Judas the brother of James, and Judas Iscariot, which also was the traitor.
17 And he came down with them, and stood in the plain, and the company of his disciples, and a great multitude of people out of all Judaea and Jerusalem, and from the sea coast of Tyre and Sidon, which came to hear him, ..." (Luke 6:13-17, KJV)
They were distinguished from the other disciples and believers in Christ.
Peter was filled with the Holy Spirit, and listed the requirements during the selection of Matthias for the purpose of replacing Judas. The replacement had to have been a witness who saw Jesus after His death on the cross (Acts. 1:22).
We are not told what happened to Matthias, and Jesus did not specifically select him. But Paul definitely "saw" Jesus after His death on the cross. Jesus selected Paul specifically. Paul was in Jesus' presence, and heard His voice (Acts 22:6-9; 23:11), and witnessed the fact that Jesus was living and risen from the grave.
"18 And saw him saying unto me, Make haste, and get thee quickly out of Jerusalem: for they will not receive thy testimony concerning me." (Acts 22:18, KJV)
Moreover, it must be considered that having lived in Jerusalem (Acts 22:3) Paul surely had been aware of Jesus' ministry before His death on the cross, and most likely had seen Him. As Paul's sister's son (nephew) warned Paul of the Jews plans to kill him (Acts 23:16) Paul's family were living in Jerusalem. As violently opposed to Jesus' ministry as Paul had been (Acts 9:1-2), he certainly knew of Jesus and his death on the cross. Paul fulfilled all of the requirements Peter listed in Acts 1:21-22.
Paul's statements in the letters recommending fellow workers, calling them brothers and "son" does not confer the select appointment from Christ of apostleship upon any of them. He called Timothy his son in the faith (1 Tim 1:2). That does not make Timothy an apostle.
Paul called Titus his brother (2 Cor. 2:13), his partner and fellow helper (2 Cor. 8:23) and his own son after the common faith (Titus 1:4). Those statements do not raise Titus to the level of an apostle. Titus was a Greek, not a Jew (Gal. 2:3). Jesus' appointments for apostles were all Jews.
Further, listing the hierarchy of the roles / functions of the workers in 1 Cor. 12:28 places the apostles in the highest authority of the workers for the gospel of Christ. It is a listing in order of authority, and does not mean that any can seek to be an apostle.
Paul exhorted them to seek the greater gift, which he explained in the next vs. in 1 Cor. 13:1 to be charity, or love. The greater gift was not apostleship, nor any of the other functions Paul had listed in 1 Cor. 12:28.
The attempt here to allow for others than those Jesus appointed to be apostles as though the function was ordinary or attainable by all is not supported by the scriptures. This also rules out any having been "selected" by Christ past the 1st century AD as no one after the 1st century AD had any claim to have seen Jesus during His earthly ministry.
" `Because of this, lo, I send to you prophets, and wise men, and scribes, and of them ye will kill and crucify, and of them ye will scourge in your synagogues, and will pursue from city to city;" (Matt. 23:34, YLT)
Matthias was a replacement for Judas who had died, keeping the number at 12.
"And about that time, Herod the king put forth his hands, to do evil to certain of those of the assembly, 2 and he killed James, the brother of John, with the sword," (Acts 12:1-2, YLT)
James was martyred before the Holy Spirit separated both Barnabas and Paul for the missionary journey in Acts 13: 2-3.
"2 and in their ministering to the Lord and fasting, the Holy Spirit said, `Separate ye to me both Barnabas and Saul to the work to which I have called them,'" (YLT)
So, the identity of the original twelve was subject to change because of the persecution. According to tradition James Alpheus was thrown down from the temple by the scribes and Pharisees and then stoned, but we do not know when that may have happened.
In Acts 14:4 & 14 Luke referred to Barnabas and Paul both as apostles as both were separated out of the church at Antioch by the Holy Spirit. However, Luke did not always refer to Barnabas as an apostle. At Acts 4: 36 -37, Luke describes the actions of Joses (Joseph), whom the apostles had surnamed Barnabas, ...
"Having land, sold it, and brought the money, and laid it at the apostles' feet." (KJV)
Luke clearly made a distinction between Barnabas and the apostles in the earlier scriptures. He made this distinction again in Acts 9:27 when Barnabas brought Saul / Paul to the apostles in Jerusalem recounting Paul's conversion on the way to Damascus. So, Barnabas was not an apostle before Acts 13, before James was martyred. Saul / Paul had already been appointed and selected by Christ as an apostle.
Up to Acts 13 Barnabas was reporting to the apostles in Jerusalem in a underling capacity, and acting as a mentor to Paul. Acts 13:1 describes Barnabas as a prophet and teacher in the church at Antioch.
Excerpt from Benson Commentary re. Acts 13:1 -
" ..The Holy Ghost said — Namely, by immediate revelation, but in what way communicated we are not informed. Separate me Barnabas and Saul for the work whereunto I have called them — Namely, the extraordinary work of preaching the gospel among the Gentiles — This was not ordaining them; Saul was ordained long before, and that not of men, neither by man, Galatians 1:1. At his conversion he was expressly called to preach to the Gentiles; and that call was renewed at the time Jesus appeared to him during his trance in the temple: but at what time Barnabas was called by the Holy Ghost to this work, is not said. And when they had fasted and prayed — A certain day being appointed for the purpose; and laid their hands on them — A rite which was used, not in ordination only, but in blessing, and on many other occasions. It was here intended to be a solemn token of their designation to their important office; they sent them away — Dismissed them from Antioch,..." Source: Biblehub
The Holy Spirit filled some gaps as the original apostles Christ appointed were persecuted and killed during the persecution to continue the work to spread the gospel.
2ND ADDENDUM REGARDING EPAPHRODITUS & OTHER COMMENTS
Paul referred to Epaphroditus in Phil. 2:25 as "your apostle."
"And I thought [it] necessary Epaphroditus -- my brother, and fellow-workman, and fellow-soldier, and your apostle and servant to my need -- to send unto you," (YLT)
Who sent Epaphroditus to Paul? The word apostle does mean a messenger, one who is sent, and this verse Paul refers to Epaphroditus as having been sent from the church at Philippi to help Paul. Paul sent him back to Philippi. That does not make Epaphroditus an apostle chosen by Christ or the Holy Spirit in the full sense of the original 12 or Paul.
Excerpt from Barnes' Notes:
"(2) the supposition that it here means a messenger meets all the circumstances of the case, and describes exactly what Epaphroditus did. He was in fact sent as a messenger to Paul; Philippians 4:18.
(3) he was not an apostle in the proper sense of the term - the apostles having been chosen to be witnesses of the life, the teachings, the death, and the resurrection of the Saviour; see Acts 1:22; compare the notes, 1 Corinthians 9:1." Source: https://biblehub.com/commentaries/philippians/2-25.htm
Excerpt from Jamieson-Faussett-Brown:
"your messenger—literally, "apostle." The "apostles" or "messengers of the churches" (Ro 16:7; 2Co 8:23), were distinct from the "apostles" specially commissioned by Christ, as the Twelve and Paul." Ibid.
Paul's use of "your" in Phil. 2:25 makes this distinction, and does not elevate Epaphroditus to the same status of apostleship as himself.
For other comments, the original question here was if the apostles had to be a witness to Jesus' resurrection, and my answer to that is still Yes. Jesus imposed that upon Paul, chose Paul for that reason, and Paul did see Jesus after Jesus' death on the cross. I never said that Paul was a disciple of Christ, nor tried to impose Acts 1:21 upon Paul. My point was that Paul knew of Christ before His crucifixion, had most probably seen Jesus before His death, and therefore having seen Him after His death could certainly witness, testify to His resurrection.
In spite of the prevalent use of the word "witness" today, no one can witness to something they have not seen. The correct definition of a witness is an individual who, being present, personally sees or perceives a thing; a beholder, spectator, or eyewitness. And, as the apostles were selected and chosen specifically by either Christ Himself, or the Holy Spirit they were eye witnesses to His resurrection.