Learn Russian: Игрок, которому я доверяю, старше, чем твой брат. - The player I trust is older than your brother.

Because the verb доверять (to trust) always requires the Dative case for the person or thing you trust. Since которому represents игрок (a masculine noun) as the receiver of your trust, it must take the masculine Dative form.

The English translation is "The player I trust." Why can't I just say "Игрок я доверяю"?

In English, we often skip the word "who" or "whom" in sentences like this. In Russian, you can never skip it. You must always use a form of который to link the main sentence to the descriptive clause.

Why doesn't старше have a masculine ending to match Игрок?

старше is a comparative adjective meaning "older" (from старый, old). Short comparative forms like this are frozen words in Russian, meaning they never change their endings for gender, number, or case.

What case is used after чем? Why is it твой брат and not another case?

When using чем (than) for comparison, the second item takes the same case as the first item. We are comparing твой брат to the subject Игрок (Nominative case), so твой брат also stays Nominative. A common alternative is to drop чем entirely and just use the Genitive case: старше твоего брата.