In every stack exchange site the domain name reflects the name of the site:
magento.stackexchange.com => Magento
webdev.stackexchange.com => Web Development
Why does Arqade differ from this? Why is it gaming.stackexchange and not arqade.stackexchange?
The domain name of stack exchange sites reflects the topic of the site. Most sites are named after their topic and so the name and domain are the same.
This site is one of the few exceptions, where a special name was chosen, that isn't just the topic. So the domain is gaming.stackexchange.com, bacause it's a site about gaming, even though it has been named "Arqade". You can also reach the site through arqade.com.
Another example for this would be cooking.stackexchange.com, which is called "Seasoned Advice".
Gaming was the original name of the site, which is why we got the url gaming.stackexchange.com. The site eventually started pulling in a lot of traffic, but both SE and the community felt that the URL and branding of the site made it difficulty to promote. So, in order to make the site easier to promote, we were given a new name, domain (arqade.com), and branding. You can find a lot of the history here and here.
The reason is actually pretty simple, the original name of this site was "Gaming beta", so naturally its URL was gaming.stackexchange.com. It was only when the site got sufficiently popular did it get its less generic, more clever (ArQAde, get it?) name. The URL remained the same as there really wasn't much point in changing it.
I should note while there is no arqade.stackexchange.com. there is redirect from arqade.com to this site (similarly there's also one for seasonedadvice.com), but I'm guessing that it only exists so its not taken by squatters or some site hosting malware.
