why is it illegal to record music from a video game?

Music, Movies, Video Games and any "interlectual work" is subject to copyright and even when you own the video game, you never actually own the copyrighted work on it. The money you pay for the game allows you to only play the game you purchased, you still must not copy, alter or distribute the product or any parts of it. You also must not play it in public, without agreement (and further payment to) the copyright holder/s. Personal use, is not a legal defense for breaching copyright laws.

Because when you purchase intellectual material you are actually only purchasing the right to use it, generally in a manufacturer's intended manner. That is what an EULA is all about. It is an acronym for "End User License Agreement." When you agree to that you are saying that you will only use the product in it's manufacturer's intended way, which is usually spelled out in the agreement. For the most part video games are intended to be played, NOT reproduced in any way. The only exception to this is with certain products that are released as "open source". Those products are intended for alteration, reproduction, copying and a whole host of other things not ordinarily allowed with full commercial products.

Even open source products generally have restrictions on what you can do with it after you have changed them or altered or copied them. For the most part the restrictions are negligible unless you intend to resell the product. At that point you would need to acquire a special license which permits that, usually one that requires you to pay royalties to the original developer. Think of it as digging for gold on someone else's land. In your case, you have purchased the permission to walk around on the land but they don't want you digging. If the product was open source, they might not mind if you dig and might not even mind if you take the gold home, but if you intend to sell it they want a cut generally speaking. It's just like when you purchase a motion picture on disc. You don't actually own the film, you own a license to watch the film. If you actually owned the film you would be able to resell it to anyone you wanted without penalty and keep all the profits without paying the actors or directors or producers or set designers or casting directors(etc.) a cent. That of course is illegal.

It isn't like owning a title or deed to something like a house or car. Those are actual ownerships. In the case of a car you have to purchase the license separately from the automobile itself. Even with a house if you own it, you still have to pay taxes on it, which is like purchasing a yearly license or permit for the right to own property.

Hopefully that shed some light on the subject for you.

its copyrighted and doesnt belong to you