Copyright is complicated.
On the Cthulhu side. Cthulhu itself, as well as most of Lovecraft's work, are open source.
On the other hand, not ALL of the Cthulhu fictions may be good to use, as a big bit of "Lovecraftian" isn't by Lovecraft but from other writers, so you have to check individually.
On the Chaosium side... They are known to be quite strict with their stuffs.
I wouldn't think they'd sell their rights to make other games. I'd assume that PC game studios brought licenses from them to make games instead.
Though I don't see why they'd be interested in letting others getting on their home turf. If they want to make a COC-system game, they'd probably do it themselves.
Your idea isn't new; Japanese Doujin circle "AlchemyBlue" is pretty much making PC games based on Chaosium's Cthulhu, and they even translated one of it into English and got on Steam (re: "Cthulhu Mythos RPG -The Sleeping Girl of the Miasma Sea-")... But they NEVER claimed to have anything to do with Chaosium, never mentioned anything about Chaosium, and probably never directly used anything originally created by Chaosium.
That's the miracle of copyright laws: System mechanics cannot be copyrighted, because they are ultimately a bunch of procedures. Then again if they can show that you did use stuffs that they can prove they created, then you'll be in a world of hurt. (Previous examples included: Sending a C&D to D&D in 1980. Had a "stern warning" to Japanese fan-made CoC scenarios a few years back, etc.)
Tl:dr, Lawyer-fights. v=3=v
So, well, you don't need to buy copyrights, and Chaosium most likely won't sell.
But you also have to triple check to make sure you didn't use ANYTHING AT ALL from Chaosium Inc, which will take maybe even more work than making the game itself.
