I'll bet on Tropico.

I'm guessing it's Patrician IV: Conquest by Trade / Patrician IV: Gold Edition.

Sim Tower was great! It's been years since I've played that game!

Grimoire confirmed?

Hmmm, a building game? Like an RTS building game or a sim-building game?

But Tropico 4 was released in 2011...
For a moment I thought GOG will finally release Settlers 1 but JudasIscariot ruined my hopes with his 'four' update :-(

Caesar IV has a download from GOG.com link on mobygames.
It redirects to Caesar III, still...
Edit: probably doesn't say much, as the same is true for Myst 4 (which links to Myst: Masterpiece Edition).

Oh, I'd love Caesar IV. I got Caesar III a few months ago but I basically played it into the ground.

Other 4s that nobdy mentioned yet:
Atlantis 4
ArcaniA (as Gothic 4)

These links are unreliable, at best. Caesar gold ( I+II) also has such a link
Caesar IV is a likely candidate though

Same case with Sid Meier's Pirates (2004).

I'll go for Simcity 4, or much better, all Simcities up to 4. Plus, it's from 2003 which I guess fully qualifies as an oldie.

Well we know it's a building game, it's a fourth game in a series, and if you build it "they will come". It insinuates that people start showing up after you make something worthwhile. Don't you govern over people in Tropico instead of have them show up if you build something? If that's the case, Simcity 4 may be a safe bet. Unless there is another game where "if you build it, they will come" that I can't think of.

Maybe Caesar IV is like that, other than the SimCity's?

Quake 1-4! Just as the hint has nothing to do with sports, similarly it actually has nothing to do with building either. It was all a red herring! It's raining herrings! Muahahahahaha!