Honestly, as others have said, any class that's "pulling its worth" in legion right now, is incredibly subject to change.
To fill in on what's performing well now though..
Unholy DK's are performing very well, they recently got buffed and I had to wonder why, they were already stronger than frost.
Havoc DH's are (as to be expected) insanely mobile and their AoE damage capability is insane, global cooldown locked from the getgo unless you pick a talent that you shouldn't. (The one that removes demons bite as a generator).
Fury warriors also have some pretty beastly AoE capabilities, can't comment on Arms.
Enhancement Shamans last i checked also had very good AoE potential, unsure if this still holds true, also global cooldown locked.
Feral druids playstyle remains pretty much untouched, unsure on their performance.
Marks hunters are currently pulling some pretty insane numbers via crit headshots. (Reports of 1.2-1.4M crits, can't verify), BM is so braindead boring, so I'm just going to say "It's bad".
Spriests are pretty damn strong in an execute phase due to surrender to madness, even more so if bloodlust/heroism is thrown in on top of it.
I didn't comment on the classes/specs i have literally no understanding or care for.
But again, all of this can (and probably will) change.
Edit: Aware you asked specifically for Melee DPS, but i just thought i'd chime in on a few other classes/specs.