I mentioned a couple of weeks ago that my first introduction to BL when I was a teenager was Shinji and Kaworu from Neon Genesis Evangelion. There have been a few Evangelion games for PC and console (and, of course, pachinko) but neither of the ones I'm going to talk about today have been translated into English, sadly.
I run a tumblr for Rin of Togainu no Chi - Lost Blood - and, as a result, I've bought and scanned a lot of early 2000s B's Log magazines over the years. B's Log covers BL and otome games, and has a 99% female readership. It was in B's Log that the developers chose to promote the Evangelion visual novel Shinji Ikari Raising Project.
Because every visual novel is a dating sim if you believe in yourself, Shinji Ikari Raising Project allows the player to have a relationship with a number of potential love interests, much as the show provided fodder for shipping multiple combinations of characters.
What's worth remarking on here, however, is that Kaworu is explicitly a love interest – there's no subtext or ambiguity here. You can date him and live happily ever after, just like with the girls.
The other game I want to talk about is Neon Genesis Evangelion 2: Another Cases, where Kaworu and Shinji begin with the highest dating affinity stat for each other, and the official character guide for dating Kaworu reads:
“While his feelings of love (愛情) for Shinji are strangely strong, his romantic affections (愛情) towards members of the opposite sex such as Ritsuko and Maya are weak. Could this be because he is an Angel? Under these circumstances, forming a ‘rabu rabu’ relationship with Shinji is preferable. As the relationship is satisfactory, concern over forming other relationships is unnecessary.”
There's also a very sweet confession scene where Kaworu asks if Shinji like/loves him and Shinji answers yes.
In another scenario in the game, exclusive to PSP, Shinji can convince Kaworu to keep living during their confrontation after Kaworu is revealed as an Angel. In this storyline, Kaworu decides to become a makeup artist, and practises on Shinji.
Kaworu: You look beautiful, Shinji.
Shinji: Really…
Kaworu: I used a green base on your eyes.
Kaworu: I layered blue on top and then the mascara…
Kaworu: And for your cheeks, a cheerful pink.
Kaworu: And for your lips, a layer of gloss.
Kaworu: An orangy pink looks nice.
Kaworu: Hehe… so pretty.
Kaworu: Like a delicious fruit.
Kaworu: I’m sure it’d taste sweet and sour.
Edited to add: I can't believe I forgot a game! Shinji and Kaworu can also romance in the PC/Playstation 2 game Iron Maiden/Girlfriend of Steel 2. It is not primarily a dating sim, but the romance content is certainly there.