All this excludes PD.
From HOL only, I ended up with 3814 to 6486 games, depending on what you count as "a game that you can play". In other words, at least one known physical or digital copy that it's documented that someone owns, or owned and reviewed. (That's just one of the many definitions...)
The 3814 minimum estimate
should be relatively trouble-free, i.e. no variants, unpublished games and the like.
But are there different numbers, say from counting TOSEC games? Says something like 20000+, but that is counting each disk and alternate crack, and it would obviously have to be unique titles and exclude platform and language variants.
I'm sure someone sits on the answer and maybe asked before, but time for an updated number?
Cheers // Photon