45 minute game...
no huge disparity in minion kills...
both teams full of glass cannons...
Their team -- has stronger "Glass cannons", champions with some innate durability, whereas yours only has Xin to fill that slot.
They have significant AoE damage output (Volibear ult, Wukong ult, Sivir Ricochet, Renektons Q and Ult, Veigars stun), while you have 5 dueling type champions (single target focus ideal).
They have a variety of CC (an AoE stun, a single target stun, AoE knockup, AoE slow+damage, Throw) while you have...1 single target knock up, 1 single target taunt, 1 single target snare, and 1 single target fear.
Looking at their scores, their Volibear performed poorly...but...this is really simple -- they had more heal, sustain, overall output capability in teamfights, better CC, and they wised up enough that they took the late game teamfights. Late game deaths matter much more than early game ones, especially in a game of that length where gold will accumulate, especially if towers are going down. They had 3 semi tanks, you had 1 -- in a sustained fight/long game, they win. You drew the match out too long, and didn't take the advantage while you had it.
It only takes one bad teamfight at the wrong time to lose a game. So sounds like that is what happened.