Yeah, Mess wasn't a fighter per se (why would he be when he got 100+ point per year), but he was a scary mofo in the Edmonton years.
He did go toe-to-toe with Roberts (in the video above), and once with McSorley (circa 1990), so it wasn't like he backed down from tough guys. Of course, he also took some liberties against players smaller than him, but horses for courses...
Not to excuse Messier's awful cheap-shots, but there were lots of guys up to the late-80s who did the same (Chelios for example, was one of the worst ever). It was how you got space, since the refs back then allowed players to strangle each other without penalties.
Joel Otto basically owes his career to Messier, since Badger Bob brought him up from US college circa 1985 specifically to counter Messier at center... at which Otto did a heck of a job. Otto was so huge that Messier couldn't physically take him down. (Otto basically did the same vs. Messier for Philly years later.)
Messier did seem to change a bit starting around 1989-90 (his best season) when he fully accepted the mantle and responsibilities as team leader. He was dishing it out less and picking his spots more, and generally was less 'wild'.
(Of course, there's also that awful cheap-shot to Modano in the mid-90s, so...)