So, it is possible that the issue was caused by an operating system that was upgraded and/or the wireless hosted network. You may believe that the hosted network is not related because you can connect to Intel® WiDi but, could this be the cause for not being able to connect to WiFi simultaneously? I mean, it is already connecting to Intel® WiDi and the ad-hoc at the same time, I have never seen the three connections working together.
I believe that it would be better to have everything as clean as possible in the operating system because this issue could be very specific and there are different variables. I noticed that you are using an older wireless driver version. So, let’s start by using the latest version 16.7 after having uninstalled Intel® Proset Software.
This article may help with your automatic connection: http://lifehacker.com/remove-wi-fi-profiles-from-windows-8-1-from-the-command-1449954864
You may also want to elaborate the question about the games in Intel® WiDi. It is normal to get few seconds of delay depending on your network environment, if that is what you mean.