The game got faster due to a few reasons. The first being that overall item costs for ad champions got reduced by a lot, and the other main reason is itemization diversity.
Now lower costs does little other than speeding up power spikes by a considerable amount, but with itemization diversity there is a big difference made. Right now there are a lot of different build paths that go into different styles of play, ranging from full on aggression to being a defensive carry. This means that champions out there are getting to where the need to be faster than before, and where they need to be doesn't affect much of how they play. A comparison to show why this would make a difference is in season 5, where you would get behind in lane (as adc). When you got behind you would either go for a BT or try to make a really slow IE, and most players would go for the IE option. Well IE only has two components that will benefit you before you have any other items. This is the pick axe and the BF sword, both of these have fairly high costs so it takes a while to build up. When you are building and IE as an adc you need a lot of farm, so when the enemy bot lane is grouping up for mid tower or dragon you will most likely not contest because you are behind. So besides contesting the only thing you could be left to do is farm, which delays the part of the game where all of the players would fight and contest objectives. But now with items such as Death's Dance, Essence Reaver, and a less expensive IE you can build your items when behind, and build defensively without sacrificing a lot of damage. So overall team fighting, and sieging as an adc isn't affected much by a weak laning phase, allowing both teams to enter an earlier mid game while being fairly even unless behind by a considerable amount. If this did not help you, I could try explaining some other things about the new meta that accelerate the game.