Primary reason for the strike is because of Formosa, which provides services for League. So they're putting pressure on Formosa via one of their most lucrative clients. Formosa had a complaint against them from SAG-AFTRA for:
The complaint comes after Formosa tried to “cancel” one of its struck video games shortly after the start of SAG-AFTRA’s video game strike. When they were told that was not possible, they secretly transferred the game to a shell company and sent out casting notices for “NON-UNION” talent only.
Edit: Official Riot statement on the strike:
League of Legends has nothing to do with the complaint mentioned in SAG-AFTRA’s press release. We want to be clear: since becoming a union project five years ago, League of Legends has only asked Formosa to engage with Union performers in the US and has never once suggested doing otherwise. In addition, we’ve never asked Formosa to cancel a game that we’ve registered. All of the allegations in SAG-AFTRA’s press release relating to canceling a game or hiring non-union talent relate to a non-Riot game, and have nothing to do with League or any of our games.