With a medium-sized room, movies and gaming being the priority, but with music being a concern too, I have to absolutely agree with Matt34 that a ported Rythmik would be my top choice out of those three brands.
That said, I have to guess from your list of options that you're looking for an $800 price point with the $900 Rythmik F15 probably already seeming like a bit of a stretch. I have to say, if a lower price is attractive to you, you might want to also consider the brand new
HSU VTF-3 MK4.
There's pretty much zero question that the eD A5-350 will play low and loud. That's eD's MO! They play low, they play loud, but they tend to have a little bit looser transient response, which tends to make them better movie/game subs than music subs. The HSU VTF-3 MK4 is roughly the same box size (just a tiny bit smaller), but it's got a little bit tighter transient response, making it sound "quicker" and giving it better delineation with music. It also costs a bit less
For the deep stuff and in terms of how loud it can play, it certainly has the output necessary for your mid-sized room. And with its tuning options, you can make it play way down low if you like - no problems there
So for keeping the price on the lower side, with $800 being the rough target, I think the HSU VTF-3 MK4 might actually be your best choice. You'll get the output and extension that you'll crave for movies and games, but you'll also get the tighter transient response and better delineation for music - it's a really nice "middle ground" without giving up much of anything on either side of the performance scale!
And there is one more thing to consider - I would highly, highly recommend that you decouple your subwoofer from the floor. Decoupling greatly reduces the annoying rattles and hums that you get from any powerful subwoofer when it is placed directly on the floor. Whenever your subwoofer plays, it physically shakes. That physical shaking gets transmitted into the floor where it becomes structure-borne sound transmission. The floor, walls and ceiling literally shake in sympathy with the subwoofer and the sound travels through the physical structure of your home. This is a big part of the reason why it's so easy to hear bass thumping away in other rooms (or in a neighbors house or apartment!) even when the higher frequencies are blocked by the walls. Bass travels really easily through structure, so decreasing that structure-borne sound transmission goes a long way to reducing the thump-thump-thumping of the bass in other rooms or apartments/houses. Happier neighbors and significant others is always a good bonus, right?
Inside your theater, there are benefits to decoupling as well. Any sound that is not coming directly from your subwoofer is technically distortion. When the floor, walls and ceiling shake, they contribute their own vibrations to the room. It's not just obvious stuff like rattles and windows and doors vibrating, there are also a greater number of both constructive and destructive interference modes as the surfaces of your room are literally making their own sound.
The end result of decoupling is that you get "tighter", "cleaner"-sounding bass inside your theater and reduced "bleeding" of the bass into other rooms or neighboring houses/apartments. For music especially, decoupling improves the quality of bass that you will hear. It is not a panacea for all bass problems, but it does offer solid, very worthwhile improvements both inside and especially outside of your theater.
For a subwoofer the size of the VTF-3 MK4 or A5-350, you're going to want the large, $85
Auralex Great GRAMMA . So just include that $85 in your price considerations, because decoupling really should be an automatic inclusion in your subwoofer purchase!
So, in the interest of keeping the price below your $800 target and factoring in your medium room size and priority for movies and games with music also being a consideration, my recommendation would be for an HSU VTF-3 MK4 with an Auralex Great GRAMMA isolation riser.
Out of your exact list of candidates that you gave, I would vote for the eD A5-350 (and eD sell their own, matching isolation riser for $65). If you are really more into getting the super-deep, super-impact, "blur your vision", "hit you in the chest" bass for your movies/games and don't mind giving up a little bit in the way of cleanliness in your music, then the scales tip in the eD A5-350's favor. I think the HSU VTF-3 MK4 is the more "balanced" approach, and certainly no slouch in delivering the deep and high impact bass for movies. But the A5-350 just goes even more in that direction, so there's a factor of your personal taste to consider there. And the A5-350 is no slouch for music, it's just not
quite as tight and clean, so just factor in your taste
Hope that helps!