Games could be prep for programming, but not for most of the very few who realize "Games are programs... I could write them, too".
Most of them will still lack logic, critical thinking, and math skills necessary for even most basic programming, let alone the often complex tasks required in modern games. Let's face it, we're not talking about simple games, we're talking about FPS games. Say "rendering engine", "frame buffer", "shader", or "vector" to them, and their eyes glaze over in sudden confusion and disinterest. The games they'd want to make don't give an accurate impression of what it takes to produce them, and the video card specs they obsess over are just numbers to them. Aside from that, there are many distinct roles involved with producing a game, which they could realize if they ever bothered to look at the game's credits.
Sure, there are "game programming" degrees available, but to me they sound pretty crap, with more focus on visuals than code. I know someone who got that degree from DeVry, and they didn't cover threading or networking. He came out as more of a digital artist than a programmer.