No. The reference to Malachi is to show the fulfillment ("for this is what was spoken of by the Lord [in Malachi 1]") of that which was described and introduced sufficiently already ("having gathered together, break bread and give thanks").
To 'break bread and give thanks' didn't mean to take a loaf, break it in half, thank God for that and go home. It wouldn't even mean that if the Eucharist was just bread and just wine. It would still refer to a significant meal referred to in summary as "breaking the bread."
It is a clear reference to the celebration of the Last Supper, when the Lord 'gave thanks, broke [the bread],' and gave it to His disciples—identifying it as His life-giving, sacrificially offered, flesh and blood (John 6:51, 53; Luke 22:19-20). Whence the command to hold it again on a regular basis as a "memorial" of the same—a term soaked with sacrificial overtones from the Old Testament; and whence the logic of the Council of Trent against the 'Reform'ers:
Forasmuch as, under the former Testament, according to the testimony of the Apostle Paul, there was no perfection, because of the weakness of the Levitical priesthood; there was need, God, the Father of mercies, so ordaining, that another priest should rise, according to the order of Melchisedech, our Lord Jesus Christ, who might consummate, and lead to what is perfect, as many as were to be sanctified. He, therefore, our God and Lord, though He was about to offer Himself once on the altar of the cross unto God the Father, by means of his death, there to operate an eternal redemption; nevertheless, because that His priesthood was not to be extinguished by His death, in the last supper, on the night in which He was betrayed,--that He might leave, to His own beloved Spouse the Church, a visible sacrifice, such as the nature of man requires, whereby that bloody sacrifice, once to be accomplished on the cross, might be represented, and the memory thereof remain even unto the end of the world, and its salutary virtue be applied to the remission of those sins which we daily commit,--declaring Himself constituted a priest for ever, according to the order of Melchisedech, He offered up to God the Father His own body and blood under the species of bread and wine; and, under the symbols of those same things, He delivered (His own body and blood) to be received by His apostles, whom He then constituted priests of the New Testament; and by those words, Do this in commemoration of me, He commanded them and their successors in the priesthood, to offer (them); even as the Catholic Church has always understood and taught.
Council of Trent, Session 22, Chapter I.
To Dr. Peter, I would retort: the term used in Malachi 1 and by the Didache is simply מנחה ("offering/sacrifice") and θυσια in Greek (the same in meaning). It doesn't refer to any specific kind. It's the simple word for sacrifice. Such as that offered by Abel, even (Genesis 4:3).
Overlooked here, too, seemingly, is the clear reference to Matthew's Gospel and our Lord's words.
Didache 14, 2 But let none who has a quarrel with his fellow join in your meeting until they be reconciled, that your sacrifice be not defiled.
Matthew 5:23-24 (DRB) If therefore thou offer thy gift at the altar, and there thou remember that thy brother hath any thing against thee; 24 Leave there thy offering before the altar, and go first to be reconciled to thy brother: and then coming thou shalt offer thy gift.
The Eucharist was viewed as the "sacrifice" of Malachi 1 by the early Church quite clearly—and the genre of sacrifice in view in Malachi, Matthew and the Didache is not ambiguous or a vague spiritual prayer, but the body and blood of Jesus is in view in Malachi and the Didache rather.
To strengthen this and tie it to the earliest Christian writers, read what St. Paul does in 1 Corinthians 1-0:16-21 (DRB), contrasting the sacrifices offered to idols by the heathens with the Eucharist:
The chalice of benediction, which we bless, is it not the communion of the blood of Christ? And the bread, which we break, is it not the partaking of the body of the Lord? 17 For we, being many, are one bread, one body, all that partake of one bread. 18 Behold Israel according to the flesh: are not they, that eat of the sacrifices, partakers of the altar? 19 What then? Do I say, that what is offered in sacrifice to idols, is any thing? Or, that the idol is any thing? 20 But the things which the heathens sacrifice, they sacrifice to devils, and not to God. And I would not that you should be made partakers with devils. 21 You cannot drink the chalice of the Lord, and the chalice of devils: you cannot be partakers of the table of the Lord, and of the table of devils.
"The Table of the Lord" is a phrase meaning the Altar, and as far as I can tell, it is only used in Malachi 1:
Malachi 1:6-14 (DRB) The son honoureth the father, and the servant his master: if then I be a father, where is my honour? and if I be a master, where is my fear? saith the Lord of hosts. 7 To you, O priests, that despise my name, and have said: Wherein have we despised thy name? You offer polluted bread upon my altar, and you say: Wherein have we polluted thee? In that you say: The table of the Lord is contemptible. 8 If you offer the blind for sacrifice, is it not evil? and if you offer the lame and the sick, is it not evil? offer it to thy prince, if he will be pleased with it, or if he will regard thy face, saith the Lord of hosts. 9 And now beseech ye the face of God, that he may have mercy on you, (for by your hand hath this been done,) if by any means he will receive your faces, saith the Lord of hosts. 10 Who is there among you, that will shut the doors, and will kindle the fire on my altar gratis? I have no pleasure in you, saith the Lord of hosts: and I will not receive a gift of your hand. 11 For from the rising of the sun even to the going down, my name is great among the Gentiles, and in every place there is sacrifice, and there is offered to my name a clean oblation: for my name is great among the Gentiles, saith the Lord of hosts. 12 And you have profaned it in that you say: The table of the Lord is defiled: and that which is laid thereupon is contemptible with the fire that devoureth it. 13 And you have said: Behold of our labour, and you puffed it away, saith the Lord of hosts, and you brought in of rapine the lame, and the sick, and brought in an offering: shall I accept it at your hands, saith the Lord? 14 Cursed is the deceitful man that hath in his flock a male, and making a vow offereth in sacrifice that which is feeble to the Lord: for I am a great King, saith the Lord of hosts, and my name is dreadful among the Gentiles.
I'm going to go ahead and say St. Paul has Malachi 1 in mind. Coincidence is out of the question. Or at least he can't have been ignorant that Malachi is the only place this is used.