Does Hebrews 10 indicate the temple was still standing when Hebrews was written?
In short - Yes!
Although it is not absolutely certain that Hebrews was written by Paul, or indeed that it was written before 70 AD, but then, as the OP suggests: If the sacrifices are not ongoing, then what is the point of the argument? A later, than 70 AD, authorship would surely have referenced the actual cessation of sacrifices, which according to Josephus, in his writings about the "Wars of the Jews" happened on 08/05/70. Note what C.C. Ryrie says in his NASB study Bible:
Authorship Many suggestions have been made for the author of this anonymous book - Paul, Barnabas, Appollos, Silas, Aquila, and Priscilla, and Clement of Rome. There are both resemblances and dissimilarities to the theology and style of Paul, but Paul frequently appeals to his own apostolic authority in his letters, while this writer appeals to others who were eyewitnesses of Jesus' ministry (2:3). It is safest to say, as did the theologian Origen in the third century, that only God knows who wrote Hebrews.
Date Various dates have been suggested for the writing of Hebrews, from the 60's to the 90's. However, it's use in the book of 1 Clement, which was written in 95, requires a date some time before that. The lack in the book of any reference to the destruction of the temple in Jerusalem as the divine proof that the Old Testament sacrificial system was finished argues strongly for a date before 70. In addition, the mention of Timothy's recent release (13:23), if it was in connection with his ministry to Paul in Rome, requires a date in the late 60"s.
Does the author intend to refer to Levitical sacrifices that are (at the time of writing) still currently ongoing? I, myself, think so. Jesus' death was to ... Make an end of sin, and, ... Make atonement for iniquity (points 2 & 3, in Dan 9:24, but the Jews went on offering Grain and Sacrifices, for their iniquities, until both were brought to a screeching halt in 70 AD.
Is there a better interpretation of the author's intent? I think not. IMO, Paul did indeed write Hebrews. Chapter 10, as in Ryrie's note section for said chapter, is all about the author (Paul) emphasizing the finality of Christ's sacrifice by contrasting it with the lack of finality of the O.T. system of law and sacrifices. Christ's redemption needs no repetition and no supplementation. Therefore a rejection of his sacrifice is final and unforgivable.
For further evidence, as to authorship, one only has to read Ryrie's further introductory points to the book of Hebrews, where he talks also about Readership (in length); Style and Contents.