So yes, as others have implied, you may have a ground loop going on, because even when you fed your scope without an earth connection….dont forget, the neutral is still connected to earth back at the installation point, and the neutral is connected to the earth node in your scope via the Y2 capacitors.
But anyway, are you connecting your scope probe ground “tail” to the secondary “ground” of your video game thing?
Maybe you are unknowingly connecting the scope “tail” to a switching node of some local switcher in there?
But anyway….as others have alluded, why not get a piece of wire say 1 metre long, and solder that to the rail that you connected to before, and see if the noise is there then (it’ll be just a flying lead antenna kind of thing)……..also, if no noise seen like that , then connect the other end of that wire to earth ground and see again if the noise is there.
Also, why not connect the scope probe across the secondary side capacitors of the transformer secondary, is the noise there then?