As can be seen in the video, White plays Rxb7+, which was answered by the illegal move Ne3+. Carlsen should have claimed the game immediately, in terms of Blitz rule A.4.2, but instead played Kd3. At which point Inarkiev stopped the clock, claimed that Carlsen made a move in an illegal position, and somehow got the match arbiter to give him the point!!
Soon after this, the Chief Arbiter correctly told Inarkiev that Kd3 was not an illegal move and asked him to continue the game. Black refused, knowing that he had a lost endgame after the Rooks were swapped off, so the CA gave Carlsen the point.
This decision then went on appeal, and the appeals committee ruled in White's favour. You can find an interesting interview with Takis Nikolopoulos and another interview with Malcolm Pein about the incident and the relevant rules. It is worth noting that from 1st January 2018 the FIDE laws for Blitz and Rapid have been changed so that the second illegal move loses the game, but at the time the game was played, the first illegal move in Blitz or Rapid lost the game.
The moral of the story is know the rules! You can download these from the FIDE rules website.
