Is it story?
Is is sexual content?
is good combat?
is it party based (j)rpgs feature?
Is it artstyle?

edit: FORGOT: artstyle.

You forgot one aspect. I suppose some people enjoy the art style of anime games?

I don't know and can only speak for myself.

I don't like anime and never watch it or otherwise care for it however it's something i can overlook in a game and still find it very enjoyable to play if i like the world building, characters, story, gameplay etc.

I understand some people won't play those games absolutely but i have found many fun games by judging them on their own merits and what they do well.

If you consider the total, even by looking exclusively at the Japanese market, they don't really prosper that much.
Yes, there are a lot, especially in the darkest corner of Japan, but they are really not mainstream or appaealing to masses.
They have their niche.

Also, I'd say that sexualized content is mostly a prejudice, there is no real data backing up the feature as going for a major feature of the products or the market.

When was the last time you found a Western animated show with a good game adaption attached to it?

I can name at least 5 good Dragon Ball Games.

I can actually appreaciate visuals and artstyle of these games. I love colorful games and prefer non realistic art, but some of those games are not drawn nicely enough for me. Like Anima Gate of Memories or Hyperdimension Neptunia.

In my case I like to watch anime but I do not like to play Japanese games. At the most I have played the games of Square Enix, Capcom and some Persona games, but no more than that.

Yes.
Yes.
Yes.
Yes.
Yes.

Any questions? For me, I don't really hate them, but I do admittedly avoid them, and for a reason I recognize isn't particularly good. For one, I don't care for the art style (I often find it too similar-looking and prefer other "western" styles which are often far more wildly varied and/or goofier), for another, I've been pretty conditioned to associate anime art style with sexual content or gratuitous "fanservice". Say whatever you want about how I'm wrong and how I shouldn't hate on the medium because of it, I already know and am well aware there's plenty of good stuff out there, but I can't deny that it affects my desire to watch anime/read manga/play games in that art style. After having a lifetime of barely ever seeing people talk about anime, on both the internet and in real life, without some sort of sexual thing thrown in there somewhere, it's probably going to take a while before I ever work that knee-jerk reaction out of me.

As Zeo noted, it's all, some, and none of those things. It's individual taste, so you can't point to one thing and say 'It's that'. For myself, I don't tend to go for the games, mostly because I hate the anime art style.

"Why do other people like something I don't?"

Individual taste, as mentioned above.

cuteness, voices maybe

If anime are niche, then everything is niche. People these days use word niche as they use hello.

I think I will give a chance to few anime I own already, then, who knows...

Is there an asshole convention on town? :P

I can't recall playing any anime games personally, besides Hatoful Boyfriend or whatever it's called with my sister, and the occasional H-game for a laugh. Before she got a stable job in the industry my sister did some art/animation work for a H-game, so sexual content is definitely at least a part of it.