Hi I'm a python developer and gamer and would love to work on this for you. I've looked into the steam API a bit and this is definitely feasible. Steam supports both querying their API for a list of servers and links that launch the game and connect you to a server. For server pings I can write some JavaScript so that users of your site get a ping relative to their location vs the location of your web server.
I have experience with projects like this and wont have any problem recreating the interface shown in your attached image. I write quality code and pride myself in good communication and providing extended support to clients to ensure that they are happy with my work.
I would be happy to discuss details and or answer any questions you might have. If your interested, feel free to contact me at any time and I'll get back to you as soon as possible.
Thanks,
Joshua Cruikshank