Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
AP Ezreal is just as viable as AD in the current patch, although in 1v1 skirmishes, AD is most likely better, but in teamfights (which win games) AP is by far superior. Combined AOE between your ult and essence flux destroys teams, and mystic shot is used to kite with rylais and to do even more than AD in some cases as lich bane proc exceeds the AD procs on mystic shot in longer games.
Simply a build, not a guide, sorry, Im a tad to lazy to spend time doing that, when I could be playing and having fun trying to master the guide I would write.