I would agree it has three dimensions if it were finite, as do all finite things. But wouldn't it be more accurately described as having three directions if the universe was boundless? I know, I know, just a habit saying we have a three-dimensional universe, I suppose. But is anyone here suggesting we have a measureable universe, at least in theory?
I'm no scientist, of course, but yes, I think that's still a possibility in the eyes of science.
Someday scientists may be able to say definitively that the universe is X cubic megaparsecs in volume (I'm ignoring any other dimensions like time for the moment) and expanding at the rate of y (i.e., dX/dt) cubic megaparsecs per year.
Despite this finiteness, we'll be able to go out and jump in our starships of the future and fly off in a given direction forever and ever, and never come to an end. In other words, it's unbounded. We'd just keep looping around and around forever, as the article says.
Of course, here too, I'm ignoring something; namely, the Big Rip or the Big Crunch, or something equally catastrophic that would prevent us from doing anything forever and ever.
Space might not be three-dimensional. How many dimensions it might have is really up to us. For the convenience of our mathematical analogies AKA theories it is taken to have from four to 26 dimensions. The sphere is a topological entity of which a convenient mental image might be earth, but that is only two-dimensional so we would have to extend our imagination to add a third and a fourth or more dimension. Four dimensions and eight dimensions have particularly rich algebras so most theoretical work is done in those numbers. In spite of popular ideas of relativity, time is not one of the dimensions and is a very different animal.