It could have been a redemption arc if it hadn't been so abrupt. Instead, it's just him being a fickle little SOB, like he always was, always being the right hand to the true power (Qui-Gon first, then Obi-Wan, then The Emperor, then he tried to make Luke his second, and when that failed, he slipped back into the familiar role of second place thug, turning on his old master to protect he new one - and die in his arms).
If you ever want a case study in both good AND bad Redemption Arcs check out the old ABC/Disney series "Once Upon a Time" - Regina's arc is mostly natural and fitting. Gold... rides a seesaw of redemption/fail/redemption/fail/oh what the heck, let's just redeem his sorry butt ... but the show really only allows two or three villains to be irredeemable, whether they deserve it or not.