How is restricted my chat on League of Legends not violating my Freedom of Speech?

You don't have freedom of speech in a private setting. You are welcome to say what you want, and they are welcome to stop you in THEIR game. You can still say what you like on your couch though.

Believe it or not but freedom of speech doesn't give me the right to come onto your private property and curse you out, that isn't how it works. I know, it's confusing......

You're free to speak your mind. You can say whatever you like, as long as it doesn't endanger someone else or deprive them of their own rights in some way. However, this is the Internet. At least in real life, you can see the people around you and how they react to what you're saying. But not here. Thus, greater care needs to be taken, because it's difficult to tell when your words might hurt someone worse than you think.

A chat restriction is the community's/Riot's way of telling you "nobody wants to hear it". It's not so much punishing you as it is a more efficient method than having everyone that's in your games mute you. In fact, it's a better solution, because you can still offer constructive comments rather than being completely unheard. Put it this way. If you go and play a pickup game of basketball, and you curse at everyone on both teams, which of these 2 choices is more efficient (for the community as a whole, not any single person):

1. Everyone else sticks their fingers in their ears for the rest of the game.

2. You get told to shut your mouth if you can't say anything nice. If you can't do that, then you don't get to play anymore.

Option 2 takes far less overall effort from the community, and interferes with far fewer people, so that's probably what should be done in most cases.

Freedom of speech is not freedom from the consequences of speech.

Riot owns the game, therefore anything happening in the game, your speech included, is subject to their rules and judgement. its like if you work at a company and you tell someone to f*** off. you're gonna get fired. why? because its part of the terms of your employment to conduct yourself in a certain manner, just like you agree to the terms in order to play league. violating those terms results in whatever consequences are laid out by the owner in your agreement.

As in you meaning like no curse words and stuff? or getting a chat ban thingy?

If so it falls under profanity and can be seen as disturbing the peace (example: drunk guy cussing out a lamp post in a public park not Jax's though he'd beat the crap out of ya xD) a threat to society aka little kids playing the game sees you type in the most "colorful" words out there and then repeating them friends and such.

You say as you wish but still have to follow societies' guidelines on whats acceptable to say to someone in public/ in general or not.

because toxic scrubs arent considered humans

Can someone explain to me kids like this think that toxicity is a constitutionally protected right? I mean honestly, what are they teaching in schools these days? Freedom of Speech has absolutely NOTHING to do with the ability to walk up to someone and tell them to eff off. In fact, it could be construed as sexual harassment and be penalized under law. Furthermore negative behavior could be construed as battery, again, breaking the law.

TL;DR Being a douche isn't protected under the constitution.

Personally, I like the way xkcd put it. Specifically, the following lines:

The right to free speech means the Government can't arrest you for what you say. It doesn't mean that anyone else has to listen to your bullshit, or host you while you share it.

Emphasis mine.

Much like retail stores reserve the right to refuse you service (most appropriately, if you're being disruptive to other customers), Riot retains the right to refuse you the use of features of their property - whether that be the chat service, the forums, or even the game client itself.

Because you said yes to the terms and agreements, and Riot's rules when you played the game.

You do have a right to free speech. You also have the right to not play the game if you choose to not honor your agreement with Riot.

What did you do wrong? Don't people have the freedom of playing the game without being harassed and such? Do you not violate their rights when doing things that get you a chat restriction in the first place? You violated a rule, which means you violated Riot's agreement with you, which in turn means they are allowed to exercise the punishment as per their rules that you agreed to by playing the game.