So, Knuth wrote this rather unusual book called "3:16" in which he took every chapter-3-verse-16 in the Bible (where chapter 3 is too short for that, he continued past the end into chapter 4 in the obvious way), thought about it a lot and wrote down his thoughts, and also commissioned eminent calligraphers to render his translations of all those verses.

(He was inspired, if that's the right idea, by the notion of stratified sampling in statistics. He called this application of it "The Way of the Cross-section".)

Here are a few extracts from what Knuth says about Philippians 3:16 in that book, which may help explain.

"English translations of verse 16 tend to be quite different from each other, because Paul's original Greek words are difficult to render in our language. A literal translation goes something like this: 'Hey, to what we've reached, by this to march!'"

(Presumably the "live up to" in the translation you quote is the "by this to march" in his literal translation. So part of what's going on is that Knuth thinks, while the translators you're quoting don't, that the notion of progress in the Greek metaphor there is essential to what he's saying.)

"Putting all these words together, we can see what verse 16 means: 'Let's keep progressing from the point we've reached.'"

(Making it more explicit. I have to say that the foregoing paragraphs in Knuth's thoughts on this verse don't particularly explain why he thinks it means that rather than, say, "stay on the same road" or "continue marching in the same pattern" or something of the kind, which seems to be the sort of idea most English versions embrace.)

"Paul's main point [sc. in this verse and the chapter as a whole] is that the Christian life is a process of continual striving for greater faith, for greater knowledge of God."

(This seems pretty fair to me. Yes, what comes before verse 16 talks about a goal, but it also emphasizes that it's a goal not yet reached, still the object of constant straining.)

It still seems hard to reconcile what the rest of Philippians 3 actually says with Knuth's "you don't race to get to the goal". (For the avoidance of doubt, in "3:16" he says in so many words "he [sc. Paul] continues to run toward the goal", so it's not like he's missed the aiming-for-the-goal idea here.) Here's my best guess at what he's thinking: Paul doesn't reckon he's reached the goal; he clearly doesn't think anyone else has reached it; indeed, it seems pretty clear that he doesn't expect anyone to reach it before their death. So (I conjecture Knuth thinks) what's the point of all that striving and straining? It can't really be that we need to strive and strain in order to be saved -- Paul seems pretty opposed to that sort of idea, elsewhere. So the real point of the striving and straining must be the effect it has on our lives here on earth.

That's my best guess at Knuth's thinking, anyway. He doesn't make it explicit, at all. Another possibility, of course, is that when he said what the OP here quotes him as saying he was only sketchily remembering what Philippians 3:16 says and attributed to it something related to, but incompatible with, what it actually says, and that if you pointed him at the actual text of the chapter and his own analysis of it in 3:16 he'd say something like "oops, yes, I shouldn't have said it said that".

(Disclaimer: I am not myself a Christian, though I was one for many years; you may or may not wish to discount accordingly anything I say about theology or exegesis. Also: my main reason for writing this comment is that I suspect that any HN readers interested in Knuth's thinking about this kind of thing would enjoy "3:16".)