I would think that the games are checked up on before they are uploaded. Either way, it is ultimately up to you as an internet user to scan your own computer given that viruses are rather easy to implant and spread.
I am sure that Armor Games does not give viruses. It is other sites that do. Armor Games wouldn't gain anything from sending viruses given that it is a free gaming website that is full-frontal with it's community.
All games are tested, I assume all links are clicked and tested as well, and the games are hosted from AG's servers. Any and all advertisements are provided by trusted parties, and while some offensive ads might slip past (those can be reported), neither AG nor the advertisement companies would be interested in losing money on viruses.
The multiplayer games, however, is your own responsibility. Don't click links you don't trust from people you don't trust. If you do, AG has no responsibility in any harm such a link might do to you or your computer. However, users can also be reported, with proper evidence (time, server, game, username used, preferably screenshots as well), and those parties would be punished or kept off the site as appropriate.
Links in comments are also your own responsibility, though they will be deleted on sight by moderators, should they be violating the rules, and the offending user will be punished as appropriate. Links leading to harmful sites can be blocked from the staff, but that would often mean a bigger amount of them as well as a big spread on the advertisers/spammers. For examples, see the hero-app spammers.
Its McAfee's Site Adviser results for Armor Games. Everything shows a green, there are no links to any red or yellow sites. Overall, Armor Games is a clean site and you shouldn't expect nor get any viruses.
