All right before we get started, just want to make sure that you all know that I haven't played any of the hack games, although a lot of my friends have been telling me to go and get the games because they are really good (from what they said)
Unfortunately the anime series are a completely different form of media so yeah this is my take on it.
Story
Honestly though, it's hard to watch an anime that where you're already supposed to know things and with the lack of background information it's really difficult to get into the story line especially when there's still so much to explain. Although it's quite fairly simple and almost identical to the other .hack stories, it focuses on the mysterious comas that's been happening to the players all over the world, and how they're trying to solve it and yadda yadda yadda it goes on. One thing that really surprised me about this is the fact that the settings is completely in the real world, I expected it to be placed in the video game because it's .hack and all but that caught me off guard when the whole thing was set in the real world. Overall, it's getting old hearing almost the same thing over and over again from other series, but the upside is there's always new information that they present about the whole .hack series as a whole which kind of answers a lot of questions from the other series.
Art
The fact that it's an OVA, the art is already given as better than worse. I do have to point out that the style of art is quite different from all the other ones though, maybe because it's an OVA or maybe because it's actually placed in the real world rather than the colourful places of "The World", either way I really have no complaints about the art.
Character
I never really saw any character growth mainly because the time spent in the whole OVA weren't really that long, it didn't take them years or months to get to the end but I would say just days, so the amount of character growth from the beginning to the end I would say was "just right" not too much but not to the point where you wouldn't notice anything. They give you a good variety of characters, but the protagonists weren't very persuasive about their beliefs or goals, they never really showed that much passion about the whole ordeal. I found them too laid back with the situations that were happening and wished they'd react in a more believable manner. There was that guy that always had a cigarette in his mouth, I've always liked characters that are like that, shows them that they too can relieve stress the deathly way.
Overall
Honestly though, with my full opinion on this, the .hack series were probably the ones that I dreaded through watching the most, but then again I think back they were probably one of the first animes I've ever really watched seriously, so it was hard form to get into it and try to analyze as much crap as I can to make a good review.
Liminality was different because they weren't in the video game for once, and that already, gives this anime a point of uniqueness compared to the rest of the .hacks!
cheers