Note I'm not arguing the main point of the article, I'm just saying that the author was less than precise in his choice of words, which can and will cause confusion in the minds of the reading public.
What he said was:
space is infinite (or at least sufficiently large) in size and almost uniformly filled with matter, as observations indicate.
I consider that statement to be plainly stated and unavoidably correct, in light of very recent discoveries. It is possible that space does eventually curve back upon itself--see how Tegmark leaves that wiggle room--but we can tell that it is at least gigantically large compared to our horizon, or Hubble volume.
Perhaps we can discuss the use of the word "universe"; Tegmark refers to the space in which we live as the "Level-I Multiverse", reserving "universe" to refer to our Hubble volume, which certainly is finite, and which contains everything with which we can in principle travel to or interact with.