Crash Bandicoot is one of those seminal video game titles that helped to define a generation. It's been revived recently as part of the Crash Bandicoot N.Sane Trilogy, but so far has been restricted to PS4. According to a video that surfaced on YouTube (and was then taken down), that may not always be the case.
In this video, a reupload of which is linked below, shows someone cycling through the menus of the game with Xbox controller prompts at the bottom. While this is hardly definitive evidence, is does certainly suggest that the devs are working to bring the game to platforms other than the PS4. And as Reddit user vxl757 pointed out in the comments of this post, it doesn't say "exclusive to PS4" on the game box.
Hopefully the game can be released on as many consoles as possible; console exclusivity is an antiquated practice that will hopefully be dead within the next few years.