I think the small form factor of mobile is more relevant than touch, although touch is also a significant factor. App design is forced to change radically to be usable at all on tiny screens. Indeed, touch is a result of the tiny aspect of mobile.

Mobile form factor and touch inputs are pretty inseparable, and are so different from desktop + pointer. A lot of subtle pain points get missed because people tend to focus on one over the other. So many desktop patterns rely on hover interactions. Touch targets need to be big enough for beefy fingers (which will then cover the thing being touched). Gesture is considered normal on touch devices but not pointer ones. Reading distance differences between mobile devices and desktop ones impacts typography. And that’s just a few basic UX concerns all before you get into the weeds of WCAG and other accessibility standards.

TL;DR - your designer needs a hug