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.
This is all about the Empower+Leap Strike combination. Trinity Force for the all the obvious bonuses + the sheen proc. Lich Bane for the AP and it's proc which is different from TF adding extra burst damage. AD and AP penetration coming from Last Whisperer/Void Staff to squeeze out all the damage you can on targets with AR/MR. Finally an Infinity Edge to pair with the crit chance coming with TF as well as give you more crit bonus+75dmg.