My thoughts:
1. The four-way should not be a requirement. As has been discussed elsewhere, anything other than a four-way is gonna hurt way more than it helps! I had an 8-way restrictor on my joystick for a short time while waiting for the 4-way and it was awful. The concern, for example, that one could "steer while climbing" with an 8-way by using the diagonals is not valid. DK doesn't acknowledge simultaneous directional inputs. You're either pushing up, left, right, or down - there is no "up-right" or "up-left."
EDIT (two years later): as it turns out, I was incorrect about this, at least in part. While I still think it's much harder to play with an 8-way, on an arcade machine you can indeed hit two directions simultanously, register two inputs, and do "steer-climbs". I was basing my assertion that you couldn't on tests I did in MAME. What I didn't know at the time is that for DK (and other 4-way games) it's hardcoded into MAME to only register one directional input at a time.
I think people should be allowed to submit using whatever controls work best for them because nobody has ever identified a control setup that would give an advantage in DK (except the old "keyboard vs. joystick" debate, where the keyboard can add a tiny bit of precision at the very, very highest skill levels of play).
2. The power supply thing is something that PSP added to the requirements when he was with TG because he noticed sometimes that certain elements of the game (the pie boards specifically) behaving strangely with certain new power supplies. I don't like this rule either. It's an extra layer of needless bureaucracy, IMO. If the power supply makes the game glitchy, it will be apparent in the gameplay. Certainly won't give anybody an advantage, in any case.
3. I like "Arcade(multi)". I think it says everything it needs to say!
4. The board is worth thinking about though, because the TKG-3s DO offer an advantage in the form of the ladder cheat. However, the title screen on the TKG-4s say "(C) 1981 Nintendo of America," whereas the TKG-3s say "(C) 1981 Nintendo", so there's no need to show the physical board because the title screen will make clear which version is running.