It doesn't matter if it is first party or third party. It just has to be exclusive to a platform or set of platforms owned by one company. You can recommend the game for whatever reason you wish.
For example if you are a Sony fan you might do something like this:
For Nintendo fans: Ratchet & Clank - colorful 3D platformer, awesome gameplay, fast-paced fun.
For Xbox fans: The Last Of Us - cinematic, great story, great graphics, and familiar gameplay.
For PC Gamers: Bloodborne - spiritually a souls game, awesome gameplay, great graphics, difficult.
Generation and specific platform don't matter, as long as the game is exclusive to one manufacturer.