I know a lot of teens and 20-somethings who passionately disagree. They say that was true about music before the invention of modern video games, but no longer. Video games help you with storytelling and solving mysteries, things music can't do.
If we're only talking about reading music, then I think the 20 somethings are perhaps correct (depending on the music or the game, I suppose). When you read music, the universe in front of you has already been crafted and it's logic already thought out and vetted by someone else (hopefully). You just have to follow along and not fall off a cliff. This is an experience I think video games can compete with in terms of cognitive load. (This is not to diminish how hard it is to read music and execute it well).
However, if we include the process of writing or composing music, I think the discussion changes. Writing music from scratch introduces a completely new set of challenges that reading music, or playing video games, don't tend to offer. Not only do you have to create your own universe, with its own set of rules and challenges, but you then have to solve those problems with harmony, melody, rhythm, textures, and in some cases, words or lyrics. I think this is a wholly different task than just reading music, and I don't think video games can offer anything close to this kind of challenge (yet).
So if we include writing or composing music in the realm of "playing an instrument", I think it blows playing video games out of the water in terms of cognitive load. It's more similar to creating a video game from scratch and playing at the same time... which sounds really hard.