You might have wondered if this is a timed exclusive and we have the answer from the devs.

“Exclusive” is a word that was commonly used during Xbox’s conference at E3 2017. But as you know, it’s less about Xbox One exclusivity and more about Microsoft’s ecosystem exclusivity. Cuphead is now a confirmed title that won’t be available on PlayStation 4.

While many games are timed exclusives or even early releases, you should now know that Cuphead won’t be available on PS4 even though it’s a third-party title. It was confirmed on NeoGAF:

Yes, this Cuphead game is exclusive to Xbox and PC (with Steam and Win10 versions at launch and a GoG release likely shortly after). There will likely be a Mac version down the road and possibly a Linux version beyond that (unless we lose our houses or whatever).

We own the Cuphead IP.