Their right to freedom of speech was not infringed upon, to suggest such is a lack of understanding on what free speech is. The first amendment allows people to say what they want/express themselves without the federal government interfering. It does NOT, however, cover state legislation, corporations, or individual responses to such action. This is similar to the fact that a company CAN and DO fire people for things they have said, and it is completely within their legal right to do so.
Now on to the other point. People are quick to judge Riot based on conjecture, but the fact is each of these individuals signed a contract that stated they will not discuss team contracts and transfers before a contract is over. This is to prevent teams from poaching. Now, I do not believe that Doublelift was attempting to poach in the long term, I highly doubt that he was attempting to convince ZionSpartan to up and leave in the middle of the season and ZionSpartan DID finish out his contract before approaching. Having said that, it would set a bad precedent to allow it to go unpunished (and let's face it, the punishment is mild compared to the six figure salary many of these individuals make), given that they directly violated the rules stated by Riot. They could have held a conversation about the future while leaving out a mention of moving to another team, specifically the team that Doublelift played for. That is a bad decision amongst any sport, e-sports included. Given that once contracts end players are given adequate time to find another team, it was incredibly inappropriate for them to have said conversation.
TL:DR: You don't have to like a rule for it to be justified, and their punishment is a slap on the wrist compared to what it could have been, the fact that everyone owned up to it shows that they have good character and an understanding that these rules are set for a reason.