One of my son’s friends can sit like that. He can also sit with his legs out at 90 degrees (the left leg out to the left, the right leg out to the right, forming a T). I had never seen anyone sit like that. When I asked his father about it he said that he was able to sit like that as a kid, too. Their son’s doctor told them to stop him from doing it because he will develop the inevitable joint problems a lot faster if he continues sitting that way.
Tell that to Jean-Claude Van Damme & Chuck Norris. 
Don’t know what it’s called.
Can’t do it myself,
Not even close.
But I just wanted to say that
You have very nice legs 
A woman I knew had a darling little girl who sat like that. Her Dr. called it sitting Frog Legged and not to let her do it.
Her mother was always pestering her to sit cross legged, which bothered me to no end. Sitting cross legged always bothered me, I never tried sitting Frog style, I just plopped on my butt with my legs out in front.
Nowadays I just sit in a chair, the floor is just too damned far down.
I am 56 and I can STILL sit that way. I don’t think it is particularly good for the knees. My legs have locked in this position and it can be quite painful until every thing unlocks. Sitting cross-legged (criss cross?) is very difficult for me. My feet point outward and I should have had corrective shoes at the very least. My spine is also extremely flexible and I can touch my elbows to the floor while bending forward.
I must be mistaken given that you can sit cross legged well, but the difference is where the toes are pointed. The pictures I can find on line of the Virasana pose have toes going straight back. Someone with femoral anteversion (or internal rotation as another word for it) has their toes point out like yours do in that picture because their knees are pointed in because that’s the way the hip rotates for them.
I can sit in the “w” position as well. Never knew it was out of the ordinary. Sitting criss crossed is fine by me too.
At closer inspection of OP’s picture I’m not sure if I can hold my feet at that angle. I will try it tonight when I’m not wearing a suit.
Unrelated, Fartprincess420, is Wu-Tang clan still a thing?
I had to actually try this toes thing. I can do Virasana with the toes in… it doesn’t feel as natural but it doesn’t feel uncomfortable or anything either. Standing naturally, my toes point slightly outward, kind of how I think most people’s do? I don’t think I’ve ever paid that much attention to people’s knees and toe directions, admittedly 
I can continue to rotate my feet outward until my toes face opposite directions at a 90 degree angle but I’m hard-pressed to make them go inward much further.
I don’t think they’re a “thing” per se, but I do get high-fived by a minimum of 10 drunks any time I am in Austin or Portland, so I guess they still have hipster cred.
I came into the thread to say this in a less technical sense. I am 40 and can still sit like this, though it becomes painful after a while now. Sitting “indian style” (sorry, what we called it when I was young) is very uncomfortable, and I can turn my feet inwards to a degree that makes some folks have to look away. So hypermobility is a possibility, but it could also be the abovementioned condition mentioned here.
I can’t even cross my legs like this:
People who can are freaks of nature as far as I’m concerned.
I can do it with my ankle on my knee though.
I used to be able to sit like that. Old age has crept up on me and I can no longer sit like that, nor do I really want to. Never thought that posture had a name, though.
In yoga I’d say about 50% can do virasana without sitting on a block. You have your feet sticking out, which is different but I don’t think it actually makes a difference, in that, if you can do virasana with your bum on the floor you can presumably do sticky-out-feet-virasana. I just tried and I didn’t feel additional strain anywhere. (ETA: oh! This article says otherwise! “The reason your student should point her feet backward in the same line as the shins when practicing Virasana is to avoid twisting her knees. Turning the feet outward (so that the toes point to the sides) rotates the tibias too far outward, misaligning the knee joint surfaces, severely overstretching the medial collateral ligaments, and, in extreme cases, possibly damaging the medial menisci.”)
The hypermobility wiki says it affects 5% of the population, which I think probably means sitting in virasana isn’t really due to hypermobility. IME far more than 5% of the population can sit like that. But the sticky-out-foot-virasana might be a hypermobility thing?
I can also do that! :3
At the time as a kid (1970s) it was a very common stretch exercise in sports (soccer, track) and school PE, and I’m still able to do it as a post-40 adult probably because of repeated childhood stretching. I’ve had a couple of folks, now as an adult, see me do it and freak out about risking knee damage or tearing ligaments, but I don’t know what the truth to that is.
Suggested name: babyonemoretimealbumcover position. Catchy, no?
I can sit like that too. I can also lean all the way back and lay on the floor with my legs like this. I am definitely double jointed FTR. And with that, I have a whole slew of medical problems with joints and such. Arthritis, hip dysplasia, spinal stenosis, etc. My advice to you is to enjoy it now and keep up on joint health. Good to find a kindred spirit who can do this too though. 
Personally speaking, if I ever met a fart princess who couldn’t do that, I’d be sorely disappointed.
Not only can I do that, but as a child I sat like that with my feet flat on the floor! Like DSeid described, my hips rotate far inward and I’ve always been pigeon-toed. I had braces and special shoes as a child without help I still tend to walk and stand on the outer edges of my feet. I have never been able to sit crosslegged and I realized at a very young age that I would never be a ballet dancer (no turnout). OTOH, I remember friends being mystified how easy and comfortable it is for me to sit in a straddle style and lean forward to rest on the floor. Since my hips rotate in, I can lean forward with no hamstring stretch.
I don’t see how I could ever be a sprinter, though, since having your knees point inward instead of forward makes it hard to run, not to mention tripping over the darn pigeon toes.
We use to call it W position. My mom hated it when we sat like that as kids. She was convinced we’d grow up with deformed legs. I sat like that every chance I got. I can still sit like that. I just asked my husband and son, and neither of them could do it. I am pretty flexible, but not double jointed or hyper-mobile.