The 1 major problem I can see with this is the Express card slot has a similar bandwidth to a single PCIE 2.1 lane and modern graphics cards use 16, though are fine with only 8 , but are crippled with only 4. So even if it runs as optimally as possible it will not run as well as mid range mobile cards maybe not even as well as lowend ones.
I just checked out your laptop specs, and it has somewhat of a weak CPU. I don't know what kind of gaming you want to try out - but most likely even with an external GPU most games will probably be able to play on low-medium quality settings.
Out of all the external GPU for laptops i have checked out - all of them were not worth the investment of money compared to what you get back in terms of performance.
Also there is no way around the expresscard requirement.