If you don't need the isolation factor, I'd stick with Open Back for gaming. M50x isn't going to give you the best positional audio, and if you liked your M40x's sound signature and wanted a step up while keeping a closed back, the ATH-MSR7 is usually better liked than the M50x from people that like the M40x. It's a bit towards the upper end of your budget, and with a modmic 4.0 without mute switch and their free shipping promotion on their site this month that ends today/tomorrow. 43+185=228, so 8 over budget.
On that budget, open back, with mic. HD 598 is a good one at your budget range, especially if you catch it on sale you can sometimes find them around 100-125. You could stick with the AD series and try something like the AD700X as well.