Freelancer -- https://en.wikipedia.org/wiki/Freelancer_(video_game)

They were going to do a sequel too. Called "Project Lonestar".

https://www.youtube.com/watch?v=Aj56okQaxZI

Sadly, Microsoft scuttled the project... Which I wholeheartedly hope they regret in the face of StarCitizen's success. :P

Age of Mythology is probably my favourite of all time. The campaign is absolutely incredible, the music is godly. It is probably the one that made the bigger impression over me.

I was about to say Half-Life, but it was ported to PS2 years after.

I think Starcraft is the one.

Red Alert 2!!!!

Bad Rats fo' sure.

Diablo, starcraft and warcraft, I think quake was an exclusive at the time as well. Elder scrolls morrowind also.

Ys I

Alternatively, Warcraft III: Reign of Chaos... 

Diablo 1 was on the PS1.
Diablo 2 is PC only.
Diablo 3 was on the 360, PS3, PS4, Xbox One.

StarCraft went to the Nintendo 64.
StarCraft 2 is PC only.

Warcraft 1 was PC only.
WarCraft 2 was on the PS1 and Saturn.
WarCraft 3 was PC only.

Quake 1 was on the Saturn, Nintendo 64.
Quake 2 ended up the Dreamcast, PS1, Nintendo 64, Xbox 360
Quake 3 was on the PS2, Dreamcast and 360.
Quake 4 was on the 360.

Morrowind was also on the original Xbox, the only console of that gen that could arguably handle it due to the shaders. - Also can be emulated on 360.

Rise of nations,red altert2
Homeworld 2