Looks like the hex-gates traveling mission is still bugged. At least in Coop vs. AI mode. I just played a game on Hextech Rift, and made sure to travel 5-6 times using the gates. After the game ended, my progress in that mission still sits at 0.
Thanks for the report, helped me track this one down. Originally I thought it was part of the Swiftplay bug, but it was separate and specific to the Hextech Rift Hexgates.
This sadly won't get fixed before 15.2, but I can confirm that the ARAM Hexgates DO work for the mission in 15.1, if you've still been stuck on it.