There is no single settings/toggle that will let you turn off/on all notifications on your iPhone. The way notification are implemented in iOS, you are limited to configure them on a per app basis only.
A couple potential solutions are:
Turn on Do Not Disturb.
This will have a side effect of suppressing any regular phone calls.
Make sure to set Allow Calls From to Everyone under Do Not Disturb settings. This will suppress all the notification banners while you are watching videos/playing games in full screen, while keeping the phone function active.
Once you have configured Do Not Disturb as above, you can easily toggle the setting via the Control Center icon.
Turn off Internet connectivity by toggling Wi-Fi/Mobile data from Settings app or Control Centre.
The second approach will have a drawback that you won't be able to access the Internet. Also, turning off Internet connectivity won't suppress local notifications.
However, disconnecting from Internet is possibly the best way to temporarily cut-off from the barrage of notification that one receives, while keeping the basic phone functionality (calling + SMS) active.