Everyone has a different definition of what it means to “crash the wifi” … but my suspicion is that your game is hogging all or most of your Internet bandwidth thereby either denying anyone else access to the Internet, or slowing them down so much so, that it’s too painful for them to use the web.
IT COULD also be a problem with your router, although 99 times out of 100 if a router is going to deny people access to a network, it will deny everyone universally and not allow just one machine and not the others, unless its been configured to give your PS4 priority traffic.
Here is what I suggest you do (in this order):
1) Unplug your router (so it turns off) and wait 2 full minutes then plug it back in and see if the problem still happens. If i does then…
2) Reset your router to FACTORY DEFAULTS - the manufacturer should have instructions on their web site showing you how to do this. See if problem still exists.
3) Borrow a router from a friend - a known good working router and try it. If it works, then replace your router with a new one.
4) If the behavior was the same with a friends router, then call your service provider and get faster Internet.