Confusion in Reducibility
Here, M2 hasn't been designed to accept Regular Languages. It has been designed to be used as argument of R. As per assumption that R can decide REGULARTM, R is free to reject M2 if the case arises. Remember, decidability includes both acceptance and rejection.

Update:
As per definition, R will accept only if argument TM accepts regular language. And, it will reject if argument TM accepts non-regular language. The setup of M2 harnesses this rejection property of R. If R hasn't rejected (as it can decide, it'll accept), it means point 2 of M2 was in action (which makes M accept w creating contradiction).