When it comes to exclusives, Nintendo is on a whole other level than Sony. I mean, you have to be a "gamer" to know that Killzone or Uncharted are Sony exclusives but Mario, Zelda, Pokémon and such are known by everyone. (Ask my mother-in-law what Gears of War is and she'll have no idea, ask my son and he'll laugh at you.)
Many of the Japanese games I like (say from Idea Factory) are out for Sony and PC but not for the Xbox. That's a big hole in the Xbox lineup but it's not about exclusives it is something else.
I don't see why Microsoft is so worried about Sony when the real opportunity is that Nintendo hasn't updated the Switch for 6 years. Retrospectively Sony giving up on the Vita looks like a big mistake and it seems something like the Steam Deck backed by a major company should be what's next but I guess everybody is intimidated by Apple and the iPhone.
That's just because Sony makes very few games themselves.
In the gaming world, exclusives usually refer to third party games, not first party games (which are always assumed to be exclusive).