so focus assist is basically like a DND ( do not disturb ) option on which is present in your phone (it behaves in the same way on windows )it will by default turn on when your on full screen and when your sharing your screen and if you put skype in priority still the notification is displayed , thats coz priority means your allowing that app to display notifications . while your gaming turn on "only alarms " so that you will not disturbed while gaming and note that only alarms can be displayed by this mode .
thx you
hope your problem is solved