PCPP is on drugs. That card is a standard single width, half height card, no different than any other lower end graphics card dimensionally. I see absolutely no reason it shouldn't work with that board or that case.
I will say though, and I certainly do NOT mean to sound condescending or dismissive of your preferences, but I am somewhat baffled by the choice of Apevia case when there are so many other, better options near that price range. The only thing I can think of is that it's a color preference that you were unable to find in any other brand. If color is not the reason for that case selection, I'd recommend at least considering some other choices.
Right from square one you can see that case has zero room for cable management in the area/compartment on the backside of the motherboard tray. Certainly it MUST be workable, as were many cases from the old days, but it's going to be a real PITA unless you plan to simply let all the cabling hang out in the hardware side of the case which is not great for cooling and airflow. Anyhow, I see no reason that card won't work, at all.
I've also found Apevia cases to be rather cheap and flimsy on the handful of times I've done builds in various Apevia models. That might not hold true for all their cases, but looking at that one I suspect it will be true for it as well.
I also don't see a need for, nor do I see any mention of any kind of adapter either on the B&H or the AMD product page for that card.
An Anandtech review of the card didn't turn up any concerns nor any adapters either, which seem appropriate since I'm not seeing any reason why it would need one.