Here's what you need to look for right now when you're buying a serious gaming PC so that you, your wife, and you're wife's friend avoid stuff like this in the future:
An Intel CPU. Forget anything AMD right now. AMD was a top contender in gaming chips about 10 years ago but sometime around the time I took a hiatus from PC gaming they seemed to have slipped far below the standard that Intel has established.
DDR 4 RAM. DDR 3 is still viable but right now I can't think of any reason to look for a brand new system that's still running last gen tech.
A dedicated GPU (Graphics Card). This is arguably the most important component in any gaming system and requires a little forethought when selecting one. You need to know what resolution you'll be doing most of your gaming at (with 1080p being the current standard but higher resolutions are becoming more common) and understand that higher resolutions will usually cost more money. (Un)fortunately there's a lot of different GPU's available so you really need to ask around to be able to figure out which one will suit your needs.
And finally keep in mind that any pre-built system is going to use the most inexpensive components the manufacturer can find but will sell it to you as though it's premium. For an average consumer this usually isn't all *that* big a deal put to serious gamers and enthusiasts it's extremely important. That's why the number one thing you'll hear when asking about pre-built systems is that you should always build it yourself.
Systems like the one your wife's friend picked up almost look like a deliberate scam meant to take advantage of "I'm not a computer person" type people. If you have to buy a pre-built system, for whatever reason, stick with reputable companies. A quick Google search for "Best Gaming PC Manufacturers" can help narrow things down.