Five or more years is a long time for any system to last and remain relevant, however, I think this system's processor is good enough to keep him content for that amount of time.
As JackSpeed mentions, the power supply is theoretically powerful enough to handle any graphics card on the market today, but I wouldn't trust it to run anything more than a mid-range card.
Regardless of what the advertising says, the graphics card that is included with this system is by no means considered a "Gaming" graphics card. It is barely above the level of current integrated graphics. While probably capable of at least running more current games at low resolutions, you're likely to run into screen freezes or lags just like your pre-teen is currently running into (depending on the games he plays).
Like JackSpeed, I'd also like to know the specs of your son's current system as well as what other games he plays. As for recommendations:
1) Take a week or two to look into building your own system. It's really not that hard and if your son is in the least technically interested, I think he'd find it not only educational, but fun as well to build a system with you. Besides, we're here to help if you get stuck! Not sure if a $630 system will last at least five years, but we could build a great core system that is upgradeable over the years (really not that different from the system you're looking at).
2) If building your own system is just too big of a step right now, I don't see any problems with the system you're looking at, so long as when the time comes (next Christmas or a Birthday), you're able to swap power supplies and graphics card (again, not that hard and we're here to help if you get stuck).
-Wolf sends
P.S. If you don't know the specifications of your son's current system, either provide us with a make and model number (assuming it's store bought), or run a program on your system called, "DXDIAG" (included with Windows). Just copy and paste the first and fourth sections of the report (System Information and Display Devices). Power supply information is also necessary, so you should take the cover off of the system (powered down and unplugged, of course) and write down the information (total watts, manufacturer and model #) that *SHOULD* be listed on a sticker on the side of the power supply.