What's wrong with me? Since 2000, almost one and a half decade, I have never, not once, worried about if my private PC can handle a game or not. And my PCs have not been expensive, $300 - $1000. Just two things: Desktop! - And always a fullsize gaming graphics card.
That's all it takes (and generous amount of RAM, of course). The performance level of a PC is primarily defined by it's age, not the amount of $. And I have routinely got a new one every third year. (Until recently. My last private PC is 4 years old, and I still see no reason to replace it).
Fullsize graphics card used to be easy in the past, - just pick one with an '8' as the second digit in the model number. Unfortunately, both AMD and nVidia have changed naming schemes since then. And that <sigh>, makes things complicated.
As for laptops vs desktops, you're dreaming if you think similar looking specs makes a laptop similar in performance. Here's a heads up for you: At work I have a brandnew laptop, type designated by it's brand as "workstation". It has the latest gen Core i7 processor with 8 virtual cores, professional graphics card and all SD drives. A (rather complex) everyday task that I have timed, takes 30-35 seconds. On my home-, four year old, six-core Phenom desktop, the same task takes 9-10 seconds. And gaming graphics is not involved.
A laptop is simply slower. That's why it, or the table underneath it, doesn't catch fire. That's why you can run it on batteries, while the desktop has this big fanned box labeled "650W" (or 1000W) inside it.