Learn Spanish (Spain): Mi afición es el ajedrez.

In Spanish, when you talk about sports, games, or general concepts as a whole, you usually need the definite article (el, la, los, las). Because of this rule, "chess" requires the article and becomes el ajedrez.

I usually use the word pasatiempo for "hobby". Is afición exactly the same thing?

They are very similar and often interchangeable! Un pasatiempo literally means a pastime (something you do to pass the time), while una afición is an interest or a passion you actively cultivate. In Spain, afición is the standard way to talk about hobbies.

Does afición mean "affection"? It looks very similar to the English word.

This is a false friend! While it looks like "affection", afición means a hobby, an interest, or even a group of fans (like the followers of a sports team). If you want to talk about emotional affection in Spanish, you would use a word like afecto or cariño.

Could I say "Mi afición es jugar al ajedrez" to mean the same thing?

Absolutely! If you want to emphasize the action of playing, you can say jugar al ajedrez (playing chess). However, just using the noun el ajedrez on its own, as shown in this sentence, is completely natural and correct.