That's just Crash, it was the fifth-gen platformer that most closely resembled those of the SNES/Mega Drive days. It's basic, sure, but I like it for that. The corridor feel is something that never bothered me- it stops it from being a god tier platformer, but Crash is satisfying enough to control (in 2/3 anyway) that it makes for a fun, breezy time.
And yeah, the spin attack seems a lot less useful in this one. It's all about that slide. I know Crash 3 has more even usage of Crash's skills, neither slide nor spin seems to get more favour than the other in that one.
Crash Team Racing is the best game in the series, anyway. I know it's unfair to compare a kart racer to a platformer, but even the standards of voice acting, graphics and music were better in CTR than any of the "main" games- that's a trick I'd like to see Mario Kart pull off one day...