Certainly, FF will produce a shallower DoF for the same aperture as M43 if all things are positioned in the same locations - photographer, subject, and background. There is no disputing that and a photographer can always crop if he isn't printing too big for the remaining resolution. It's easier to pick the right time to fire the trigger if you can fill the frame with the subject because you can see it better in the EVF or LCD and the background will be more out of focus if you do. If you use a shorter FL the background will be less defocused. That's a point I'm trying to get across.
A longer FL to fill the frame more with the subject will blur the background more so if you use a FF camera with a shorter FL it will reduce the difference in the subject separation - the DoF difference between FF and M43. FF may not give you a more defocused background - or not much more depending.
That's why I'm saying there is more to this than the camera gear. It's the reason I get a very defocused background if I shoot a hood ornament on a car at 150mm and f/5.6 with an M43 lens. If the lens will enable me to focus closely with the lens I can. It is an attribute of Olympus zoom lenses that they focus more closely than other brands for the same focal length. I think this is a reason why they are designed to.
Translate this to the skate park. If you shoot the skaters at 100mm (200mm FF) with an M43 lens so you fill the frame more vs. shooting at a 70mm fl with a FF lens this will narrow the DoF difference.
Now forget the IQ for a minute and look at these images below. I walked into my living room and took these snaps with an OLY 14-150mm f/4-f5.6 lens. A midrange consumer-grade lens with an MSRP of $550. It's weather sealed by the way.
At the short end it's as sharp as both the 40-150 f/4 and f/2.8. At the long end it isn't. If I need feather detail I would not use this lens at the long end but for sports, it's perfectly sharp enough for me. Depending on the circumstances, I can't tell if the PRO lens image is sharper unless I crop 100% and sometimes they are still very close, so close it doesn't matter. I can use this lens for sports but usually, I take something faster because if I'm caught in rain and gloom f/5.6 might not be fast enough. F/4 is. I always take the 14-150 as a travel lens especially if I have one body because of the range. It's tiny for the range, half the size/weight of a FF lens of the same range. Sometimes I don't have time to change lenses especially if I'm in a car. I have great images taken with this lens because of the range. Photos I would not have because I didn't not have time to change lenses. I could live with this one lens if I had to. It would not be ideal. IBIS works better at shorter FL so at f/4 and 28mm I can shoot a very slow shutter speed. Not for indoor sports but for indoor events I use it.
Forget IQ for a minute because I pulled this lens out and took a few snaps in my living room to demonstrate DoF, not to make great images. Look at them.



Now here is the background in focus and the foreground out of focus at 14mm to show you the room I took the other three photos in:

Did you think you could defocus this background as f/5.6? The green plant just behind the altimeter/clock is only 7 feet away. It's a smooth, green blob in the top photo. The bokeh is creamy and pleasing. You can't make out anything in the windows, not even a window or the trim. Not the pottery, the chaise or chair, or a lamp if I put any of them in the background and shoot the clock a foot away at f/5.6.
Did you think this was possible at f/5.6 with an M43 lens at 150mm? The reason you can is this lens focuses 12" away at 150mm, even closer at the wide end.
You read the specs and reviews and comments from photographers posting on DPR and think - FF makes shallower DoF for the same f-stop and it does, but to know how it will work for the photo you are making, you have to know it is also dependent on the distance between the subject and the camera and the background and the camera. In this case, where the clock is 1 foot away and the plant is 7 feet away. The plant is very focused.
Map this over sports. Of course you won't be 1 foot away from the subject but if you can shoot the subject at 100mm or better still a 150mm with an M43 lens vs. a 70mm FF lens it will narrow the DoF gap. How much I'm not sure. I never shot a skate park but it's possible to me that a 150mm f/4 M43 lens will blur the brick building as much as the FF camera did in the original post and the f/2.8 M43 lens will blur it more but not much more. I do not believe similar results are impossible with the M43 system.
Further, I suggest you can use the 75mm f/1.8 Olympus prime lens in this situation or the 45mm f/1.8 prime lens which is a little longer than a 24-70 FF zoom. And you can try a 25mm f/1.8 Oly or Panny lens because these lenses are very inexpensive, very small, very light, and very sharp. You can own all three of them for the cost of an f/2.8 Nikon zoom or less. Now you are shooting an f/1.8 M43 prime lens against a FF f/2.8 zoom lens, picking up a stop. You can buy both M43 lenses - the 45 and 25 for ~ $700 new and take both because they are tiny. Add the 75 for another $500-700 and you have three fast M43 primes for less than $1,500.
If you find 17, 25, or 45 in M43 is the right FL you can buy one in f/1.2. Then you are shooting SHALLOWER DoF than you are with your f/2.8 FF zoom with your M43 kit.
These are expensive lenses if bought new but they are tank-built and can be bought used for very attractive prices. $700. They make creamy defocused bokeh. But they are so bright they have to be stopped down or used with ND filters on bright days.
Zooms are more flexible but if you know the venue and you position yourself for panning shots where the skater is moving across your field of view or you know where you want the skater to be when you take the shot you can put yourself in multiple positions where this will work with a specific prime lens.
I know the road race tracks where I shoot. Sometimes I take the tiny OLY 45 f/1.8 or 75 f/1.8 which is an incredible lens. I use them instead of a zoom to give my shoulder and arm a rest where I know the photo will work at these FLs. The results are excellent. On bright days I have to use ND filters to prevent the lens from stopping down into diffusion when I'm panning with a slow shutter speed in bright sun in the desert and/or shoot on ISO LOW but it works. Now with the f/4 zooms and never need a rest so I don't use the primes. When I shot f/2.8 40-150 I did need them.
I never shot a skating park, but I think a sharp subject and a blurry background is possible with an M43 kit, certainly a background as blurry as the brick building in the background in the original example.
Can't shoot shallow DoF with an M43 kit? That's a myth.