I believe this is because Wii VGA cables are NOT VGA cables. They’re YPbPr over DB-15 cables – some devices (mostly projectors) can take in component video over their “VGA” port; VGA expects R+G+B+Hsync+Vsync signals, while component is only three signals (Y + Pb + Pr, though it may be able to do R + G + B over the same pins; I don’t know off the top of my head). Therefore, the VGA cables will not work on most displays unless the display is built to take component in via the port – I’m pretty certain this is not the case for the Asus, but I don’t have first-hand experience with it.
You will need a proper active conversion box, like the devices you linked. I’ve only personally heard people claim that this device has no lag, but… again, I don’t have the personal experience, so I can’t promise anything. If you end up getting a device, and can properly test it (split the component signal and videotape it side-by-side with a CRT, then do a frame-by-frame to see if it’s lagging), that’d be really useful info to share (I know I’d love to hear it). I don’t know that the VH236H has been tested for lag over HDMI at 480P off the top of my head, which is another concern (the upscaler) that could introduce latency, so… I guess all I can say is good luck, and I’d love to hear your findings.
All that being said, knowing the Smash community (I used to roll deep with my local Smash scene a few years back)… they’ll complain no matter what. Unless the scene has changed, if it’s not a CRT you’ll get complaints (even if it’s lagless, people love to have something to blame their losses on). You may find it easier to ask around for four more CRT’s from people, or go down to the local pawn shop and grab some more; that way you don’t have to worry about lag, OR people complaining thereabout. It’s just the nature of that scene, in my experience.
EDIT: Huh, RoboKrikit’s statement changes things RE: the VGA cables. Maybe the VGA ports are more tolerant than I thought; I’m just going off of my basic knowledge of the signals, but it’s possible that more monitors are tolerant of the off-spec usage than I expected. Might be worth grabbing a set of those cables for myself, just to see what they’re doing. If the Green cable carries a “Black and White” signal, that means it’s the Y line (which carries Luma + sync info together on one line) of YPbPr, so the Wii isn’t changing to RGB outputting… and as looks like it’s a passive cable, it must be all in the YPbPr colorspace (not converting to RGB)… so I guess YPbPr over D-Sub is more common than I thought. Apologies if I provided inaccurate information. Good luck figuring stuff out, and let me know how it all turns out!
Learn something new every day!