Learn Spanish (Latin America): Sinceramente, el infiltrado se juega mucho. - Honestly, the infiltrator is risking a lot.

This is a perfect example of a lexical shift in a pronominal verb. While jugar means "to play," adding the pronoun se to make it jugarse changes the meaning to "to risk" or "to put at stake." The infiltrator isn't playing a lot; he is gambling or risking a lot.

Could I just use arriesgar to mean "to risk" instead?

Yes, el infiltrado arriesga mucho means the exact same thing. However, jugarse is a very natural, idiomatic way to express this in conversational Spanish, especially when the risk feels like a gamble. You will also frequently hear it in phrases like jugarse la vida (to risk one's life).

Why doesn't mucho change its ending here?

In this sentence, mucho is acting as an adverb telling us how much he is risking, rather than describing a noun. Adverbs are invariable in Spanish, so it stays in its default form. If he were risking "many things," it would act as an adjective and change to match that noun: se juega muchas cosas.

Is sinceramente used exactly the same way as "sincerely" in English?

It depends on the context. At the end of a formal letter, it does mean "sincerely." But when placed at the beginning of a sentence to introduce an opinion or a blunt fact, it is used exactly like "honestly" or "frankly" in English.