Stephon386 A gaming laptop is a bit cheaper than a gaming desktop at the moment. But laptop hardware is also weaker than desktop hardware in the same class, for example a desktop RTX 3050 is about 50% faster in gaming than an RTX 3050 mobile. (That is only an average, and there is some variation from one game to another even before you start factoring in different graphics settings.) So in terms of pure performance, you're getting more for a desktop than a laptop.
The other important point to consider is that a desktop is much more repairable and upgradable than a laptop. You can replace any single desktop component and keep most or all of the others, whereas you can only really replace RAM or a drive in a laptop. So desktops will last longer, on average, rather than the traditional 3-5 year life expectancy of a gaming laptop. They're lasting longer these days, again on average, but still can fail in a few years. Or they can last for a decade; it's really hit or miss.
At any rate, you won't typically find a new (true) gaming desktop or laptop for $500 U.S. outside of Black Friday and holiday deals. Some computers are listed as "gaming" but don't have gaming hardware. These and more typical non-gaming systems are a significant drop-off from a gaming computer, usually capable of high graphics settings at best. That's not to say they're a bad choice, only that there's a clear difference in performance for a relatively small increase in price.
Having said that, I do see this gaming laptop (only a few left?) for $550, if you're interested:
https://www.walmart.com/ip/9969804547
All else being equal, I would say the cheapest desktop I linked earlier is the better purchase in terms of both current performance and future repairs/upgrades. But this is definitely a viable option, and it's also a good example of what you can find if you're looking closely at sales.