The riddle describes
the process of solving a Rubik's Cube rapidly (something on which Emrakul is an expert) under competition conditions.
Argh! I think I must be going mad!
Beating others in a fevered dream -
I assume it's a pretty intense experience. Beating others, of course, in the sense of solving faster than they can.
Colours whirling, twisting, changing,
Digits blurring, causing pain.
The colours of the cube faces. Twisting because that's what the faces of the cube do. The digits are the solver's fingers, blurring (and in pain) because they are moving so fast.
Experts say the tiger-owl is king.
Emrakul's profile picture is of a lovely origami owl -- and before that, so I'm informed, it was a tiger. (And Emrakul is a very skilled cuber.)
Finally success is found!
Gasping, I survey my work:
Cube solved. Phew!
Happy faces, no more blotches,
I think I've cured them all in time.
The faces (of the cube) are now the way they should be, each its own solid colour. The mismatched colours have all been fixed, and I might even have set a speed record.
Just tell me: what's it all about?
I don't have an explanation for the A..J at the starts of the lines, but I am informed in chat that that's OK because it was done just for fun and not meant to clue anything :-).