I think it's worth putting here that since the website came back online on 2024-04-01, this solution no longer works. Even if you switch your VerifyPeer pref to "0", you cannot access PQ online from OS X 10.7–10.11. The only way to play online on Mac now is to use either macOS 10.12, 10.13, or 10.14. I'd be very interested to hear whether anyone else is still even using the native Mac version of PQ in 2024. Even I mostly use WINE on my 2021 MacBook Pro, only switching to the Mac mini when I really want to play a level with a lot of PQ features in it (the trees and cannons and gravity triggers in particular drop frame rate on WINE heavily).
I do still have a partition of my Mac mini on OS X Yosemite, for highest frame rate, but since I can't use it for PQ anymore and have stopped playing MBG as much, I don't even know whether it's worth it to keep it. Mojave still runs well enough for the light use I currently have for that computer. If you are wondering whether to choose between Sierra, High Sierra, or Mojave, I'd say Mojave is the best choice, unless you really need the best performance possible, in which case you'd use Sierra (or High Sierra if that's what your Mac came with).