While sure, it'll run Skyrim through Wine via Linux, it will be on low with an unplayable frame rate. If you want something that can play games, cheapest laptop for that i can think of is $600:
While Chromebooks are great for web surfing, that's really all they're great for: a low demanding task aimed at those who just want to sit on the couch and browse the web. No games.
I don't know if this specific machine will run it or not, because I don't know the exact specs.. just to help give a little perspective to those who gave an emphatic "no" without explanation or elaboration, or said Chromebooks were only web machines, here's a video of an Acer Chromebook running Skyrim on Ubuntu 13.10.
These machines are a lot more capable than the average person realizes.
And take this for what it's worth, because this is just a random video I found when trying to see if this had already been discussed.. but it appears to a guy recording himself playing Skyrim on a Celeron 847: https/www.youtube.com/watch?v=3kcsvQJvbpM
I personally haven't played skyrim on my chromebook as I worry about the heat it will produce and the longevity of my cpu and battery. Maybe in the future this maybe possible as I do know there as some chromebooks out there that have i5 cpus in them.