You don't have to be a government body to agree with free speech

Edit: Since most of the comments are from people who only read the first paragraph, please read the entire thing before pretending you know what you're talking about.

Most often, the argument against free speech is that you aren't "protected from the consequences." That's, first and foremost, a lie. Freedom of speech from a government perspective is not limited to you being physically able to voice your thoughts-- if that were the case, the only way to "take it away" would be to paralyze you completely. With the actual meaning, however, you are protected from the government enacting an unfair consequence like throwing you in jail after the fact. (I feel deeply sorry for those on the European servers who live in countries where you actually can get thrown in jail for mean comments on the internet)

That said, private communities can limit that right if they so choose. Your parents can throw you in your room if you decide to curse at them. Websites and games can, without any prior warning needed, ban you for using certain words. But what that means is that they are against the idea of free speech as it pertains to those they have power over. They believe it is their duty to punish those people for the betterment of either themselves or the community at large.

Riot does so for both reasons. Banning players deemed to have used their uncensored chat function in an unfit way allows them to look like they are a good company to the small group of people who also disagree with free speech in this context while those who agree with it don't particularly care as long as they aren't effected themselves. They also believe that it leads to a better community, though the evidence that only 0.006% of the community gets banned while League is still known for having the most toxic players for a non-voice-enabled game goes against that belief.

And they are free to do so, but it shows that they are against the idea of free speech for the people they hold power over. They don't have to allow it. They are free to be, and are, very authoritarian in that aspect.

As a final note, they do technically allow you to type whatever you want in the chat. As I said at the beginning, that does not mean you are free to. That only means that they don't want to do the work to make their censors match their guidelines for punishment.