there's actually tools for this I think. packets can designate priority. I think its called Quality Of Service. for example e-mails and your 'civilization' turn say 'don't worry, slip me in when you have a free millisecond, I can wait a minute if you're really fucking impacted', streaming video and other suff with some leeway says 'I got a schedule here' and calls or your 'call of battle strike' game where the thing is badically useless if its late cut to the front of the line.

not every router implements it, and that's fine. unless I just imagined all if this. its been a while, but the people who designed the bones of the internet were smart and forward thinking. for example the problems with address space and stuff ipv6 was implemented to solve was finalized in the 90s. the corporations hadn't ruined everything yet.