let's
break it down, shall we?
motor -ist. If we are to believe Webster 1913, the suffix "-ist" denotes being an "agent", a "doer", one who practices, or "a believer in".
So, is a motorist is a "doer of motors". (sort sick, huh?)
Alright, now ignore all of that bunkum above; a motorist is a "driver" of automobiles.
There, that wasn't so bad, was it?