Gay games
There is an RPG for the PSone (also playable on PS2) called
Suikoden II
which is supposed to have a very emotional 'bromatic' storyline, I've never played it because it's hard to find and costs a fortune on ebay...but if you have the money you should get it. I've only read about it but people say the characters are covertley gay.
Many speculate this series deliberately tries to appeal to fans of gay/boy-love manga in Japan . This very evident in the character design for the most recent game
Suikoden Tierkreis for the DS(DSi).
Anonym to media.ds.ign.com/media/142/14275824/vids_1.html
Which is easier to find, it's currently available in stores. I don't know how old you are(I'm 32) but Nintendo is coming out with a DSi with extra large screens in the spring so I would recommend you wait 'till then as it will be easier on the eyes. It's not a gay game but aesthetically it is basically a game staring a bunch of pretty twinks. It may not overtly gay themed but the characters will appeal to you.
For the same reasons I would also recommend
Final Fantasy XII (12) for the PS2. The character design is obviously gay friendly and the boy staring in the game just gorgeous to watch...for hours and hours. May people also suspect that there are gay artists involved in this series because of the some of the character design.
Anonym to ps2.ign.com/dor/objects/488222/final-fantasy-xii/images/111803_vaan_ashe.html
All these are RPG's and are easy to play.
Besides that I would also say
Bully, you can find a used PS2 version but it also has an exellent Wii version. It's a real gem of a game which got great reviews and the boy kissing never gets old:
Anonym to www.joystiq.com/2006/10/22/boy-on-boy-kissing-in-bully/
reviews on Bully:
Anonym to www.metacritic.com/games/platforms/ps2/bully?q=bully
Hope that helps.
So thats Bully, Final Fantasy XII and Suikoden II for your PS2. But if your really want to explore new games I really think you should get an new system like an Xbox 360 or Wii and a DSi.