Nope, the wallrun is just mentioned to explain how Cain can reach certain places without being able to fly.
There's a bunch of tricks, though:
- Flapping rapidly makes the vertical distance you can cover greater.
- One area has invisible blocks you can trigger by jumping into them from above (it's an outdoors area so it might not be the place you're in).
- Some areas has fake walls, so there might be an alternate path. All of these are indicated in some way if you're on a lookout for details in the environment.
- There should be an easter egg that gives you infinite wing flaps, but it was added pretty late in development, is very obscure to find, and isn't required for anything.
There also used to be a bug where if you get hit by an enemy instantly after jumping, the momentum of the knockback and the momentum of the jump would stack together and you'd be sent flying very far.