LoL VS event 2018 last Darius quest
It seems to be bugged - I can confirm that ARURF does not count towards the completion of this quest. Both myself and a friend of mine have both had the exact same problem, where we win a game of ARURF which satisfies the requirements yet we don't get the unlock.
All other matchmade Summoner's Rift game modes should count, however. This includes Co-Op Vs. AI games, which is a quick and guaranteed way of finishing the quest.