The quick answer is no, there is no cross-sport prohibition in most sports leagues. The long answer is that almost anything can be negotiated and that player are usually willing to make concessions in these deals in turn for more money.
Many modern sports contracts have clauses in them that protect the employer if an athlete is injured doing an athletic activity outsider of their normal training. A good example might be a football player blowing out his knee playing pickup basketball. These clauses usually give the team the ability to withhold future salary or even go after previously paid wages. Although these clauses aren't always exercised depending on the player's relationship with the team, the severity of the injury, and the activity that caused the injury. A team doesn't want to risk alienating a player or their fans unless there is a huge gap between the financial impact of the injury and the player's future perceived value.
There are also various sponsorship agreements that players and teams have with companies that have restrictions about supporting a competitor. For example an NBA player sponsored by Nike might not be allowed to wear an Adidas shoe during a game.
Considering these precedents and that Riot appears to act as some combination of a sponsor and team/league that employees these eathletes, I think this decision is pretty reasonable.