I think you can, because as far as I know, you can host the flash files of games AG has.
Taken from Help Section:
Can I download the Flash files for my own website?Sure you can! All the game are available on the Free Website Games page. You can either host the content yourself or use the provided embed code to get a direct link to our content. If there is a game not on this page, please get in contact with us.
Technically, most of the games other than those developed by the Admin team aren't owned by AG, best to ask the developers directly. I'm sorry, but I really can't understand your question apart from that.
Generally, you will need approval from the developer. That is, the creator of the game, nor the one hosting it (in this case, ArmorGames). I recommend you try and look them up to find a way to contact them and ask them directly. However, otherwise, you can only put games put in the "Free Flash Game" section, as those are the only ones AG wants spread like that without explicit approval.