We have some great cats at our house and they interact in the most unique and entertaining ways. Sadly, most of that interaction happens at night. There is one of them, though, that interacts with us during the waking hours: Ginger (a ginger-colored cat, as you might expect). Once in a while (probably about once a week), Ginger will decide that she sees dead people or something equally dreadful. Her pupils dilate and her ears tilt back and she takes off like a rocket, tearing around the house with reckless abandon. You just know she's having fun. We are, too, as we cower in the corner of the sofa or recliner hoping she'll be airborne and at a safe distance as she careens past your face or legs. It's rare fun.
Another cat (Smudge) interacts with my wife particularly at night. She plays a game kind of like Whack-A-Mole, but it's more sedentary. It involves Smudge trying to create an airtight seal across my wife's nose and mouth with her soft underbelly. My wife has started to suspect that she is allergic to cats since this game appears to impact her free flow of air, but I think she's just addicted to breathing. I'm tempted every so often to find out how the game is progressing, but I'm not sure that my wife would interpret my attempts to wake / revive her with the best of intentions.
Another cat plays a night-time game with me. I'm not entirely sure who this is, as I'm usually not awake for the announcement of the line-up. It's either Herschel or Cola. This game is called "Are You Smarter Than a Cat, Fool?" or something like that. I'm not yet good at translating feline. In feline, its called "Meow, Meow, Meow, Bitch!" It's played like this. 1) The human will pour himself a glass of something liquid to drink during the night, should he wake up thirsty. 2) After consuming some (or not, it's immaterial in the big scheme of things), the container is set by the bed. 3) At some time during the sleeping hours, the mystery cat will discover the glass and knock it over. It's possible the cat will drink some of the fluid through the process of sticking his foot in it and then licking his foot. This could also be a grooming method. The drinking and/or grooming act is immaterial to the process of the game. 4) The sound of the glass (usually, but not always, a plastic (unbreakable) tumbler) hitting the floor will waken the human. Hilarity ensues (if, by "hilarity," you mean Lights, Cussing, Action (mopping, etc), angry verbal exchanges by other humans collaterally woken by the first human involved, and a few gentle little love-"nips" certainly not intended to break the skin by Micah (aka Methuselah) -- the chihuahua that sleeps with and apparently guards my wife from me when I'm ambulatory but not reclined RIGHT NEXT TO HER!). The other night while playing this game I awoke to see a cat observing the half-full glass of soda. I determined this to be the one night I proved I was, in fact, smarter than a cat. I reached for the glass and held it for a while, intending to replace it once the cat lost interest and walked away. I awoke just a few short minutes later as I spilled the contents onto the bed and floor, relieving the cat of that task. Hilarity ensued. Last night, I AGAIN proved the cat was smarter. Sigh. No real hilarity, though. The volume was minimal and I just threw a towel on the spill. By the way, lidded cups with straws don't work -- they simply break upon impact -- and I'm too proud to use a toddler's sippy cup. I heard a colleague mention that his young son requested a drink holder by his bed. Hmmm... maybe I can avoid the hilarity that way.

Gotta love cats. We have three. Spooky, does much like your Ginger. She seems to just decide, out of the blue, that it's time to fly around the house for a couple of laps. We just try to stay out of the way. She loves TV. Football, basketball and weather forecasts have her in front of the TV pawing at the screen at unbelievable speed. And she loves my wife's spot on the couch. It's a game of cat-and-wife to see who gets to sit there.

Harley wants me to sit or lay where he can lick my head. He wakes me up often licking my head. Cat tongues hurt. It's like having my head sanded. He also likes to be covered up. We keep a throw on the couch for him to get under and when we turn over at night we have to be sure where he is first. He also waits by the shower door and wants in the shower just as we get out. He just watches the drain. Not sure why.

And we have Willie. He has no use for my wife whatsoever. Absolutely a daddy's cat. Wherever I am, he is. I trip over him at least a dozen times a day. He can't stand for me to be on the computer or the phone. He gets right in my face and meows like he's telling me he's not getting my full attention. I haven't gone to the bathroom by myself since we've had him.

My cat used to exhibit the same behavior as you describe Ginger having. We always said she was fighting the invisibles.

That's the way it goes, with the cats I know.