I worked at an aquarium store in high school and owned saltwater tanks for decades. Some fish do get something like the zoomies where they will dart around the tank. I had a wrasse that would get excited in way that didn’t seem frightened but more like playful.

I don’t know about “tag” per se, but they do sometimes have territorial sparring which is more like swimming up at each other quickly and trying to chase each other away from their spot, without it ever really getting violent. If one of them didn’t chicken out though I imagine fins would get bitten.

My clownfish would come up and nibble my hand if I put it in the tank and I could scoop her up from underneath with one hand. It was not so much playful though, she probably just associated my hand with food so she’d hang out as close as she could get until I gave up the goods. Clownfish have instinctual behaviors that encourage them to rub up against anemones, so maybe she was treating me like her weird semi-aquatic anemone buddy.