A computer i can buy that is around 450 pounds? It has to be a gaming computer?

The computer from the link you provided would be fine for Battlefield 4. A HD7750 card is plenty, and you can look up lots of examples of BF4 gamers using that card
(just google search "Battlefield 4 HD7750 youtube").

You may not be able to use the highest settings… But that is always a trap when it comes to PC games. There's about a 5% difference in quality between medium settings and ultra-high settings… And about a 200 pounds difference in price. Modern games are always designed so that they will work on as many computers as possible, and the ultra-high settings are positioned so that only very expensive cutting-edge computers could possibly handle them. Of course, to get those ultra-high settings you have to pay through the nose for gear that will be considered average within a year, and low-spec within two years.
Set a reasonable price limit, and get something that will get you up and playing.
If you are willing to pay a bit more than 429, then you could take a printout of that computer spec to most computer stores, and explain that you want something like this, but with a faster graphics card. One of them is sure to give you a similar deal… Same thing, more graphics, for maybe 500. But you'll hardly notice a difference.

The computer you have listed looks about right for that price. You will be able to comfortably run any game out there, plus anything released in the next 3 years.