I don't know if "universecentrism" is a word outside of this post. In cosmology, it's called the (weak/strong) anthropic principle or otherwise more generally, anthropocentrism.

I disagree with the author that it is more likely correct than previous, smaller-scale versions of anthropocentrism.

It would be unfathomably unlikely if we lived in a universe with the size, extent, and homogeneity of the one we observe, and be the only region that developed life and intelligence.

Is a big leap of faith, a statement we don't really have enough data to assert yet, I think. There are still many plausible explanations humans might be in the position we are as the "only known intelligent life" in the universe.

1. The definition of the phrase itself varies hugely depending on the meaning of each of those 4 words

2. We could be the only "intelligent" life in the local area of the universe, but not the only in the whole universe

3. Given the exponential rate of technological advancement, the simultaneous existence of local intelligent life might be intrinsically unlikely, but not an indication of human exceptionalism in any way

4. We only seem to envision life that fits the parameters of this universe well because we have the most experience with it. It might be that many universes are capable of supporting life in ways we aren't considering. Etc.