DFC made this claim based on its PC Game Meter service, which draws data from multiple sources. The service does not include browser and casual games in its report.
Update: Riot Games contacted us to say that DFC has retracted the report press release. GamesIndustry also posted the following update: "According to a Riot Games spokesperson, League of Legends sees 'over 500,000 peak concurrent players every day on just the EU West shard,' which doesn't even touch on players in the United States. This is contrasted with the 325,879 players that Valve's Steamgraph shows as the all-time high for Dota 2 beta."