Well, this question starts to get into some unusual areas in American Constitutional law. To give a basic, blunt answer: yes. Speech is protected by the First Amendment. If the government tried to break up a peaceful rally, there would be popular outrage and likely some impeachments.
However, media like films and games are not purely speech. They are, first and foremost, commercial products. As commercial products, they fall under the Commerce Clause, which gives Congress the power to regulate commerce between the several states. So for all of the clamoring from the industry about how their products are protected by the right to free speech, they can be regulated as commercial products. In that sense, video games and films are more like cigarettes than speech. There are many regulations to selling cigarettes and hypothetical future legislation may ban them, but for now they are legal.
So really, the government isn't deciding what speech is protected. They are deciding what is speech. Personally, I think any product whose primary purpose is to turn a profit cannot be called "speech". It's like trying to justify insider trading as "speaking out against regulation of the market". As as for their power to decide what is speech, there are many, MANY groups dedicated to keeping the government in line in regards to that. The ACLU, for as much as I detest them, is particularly useful in cases of free speech.
