SO, the TC is working properly
more than enoough room for the belt at idle, moved all the way down on the driven at high rpms.. sounds perfect; video would confirm that, but let's just say it indeed is all good here.
Now, what about the sprocket on the driven? is it turning properly or not?
If it is (what I assume) is the chain moving?
and what about the axle sprocket?
If everything is moving except for the wheels, check that you mounted everything correctly (key stock missing on the sprocket holder or wheel hubs for example)
If the chain isn't moving, check that it sits perfectly on the sprockets;
if the small sprocket on the driven isn't moving, make sure that you installed the driven is mounted correctly to the jackshaft.
'sid
PS please, let us see some pictures of the single parts, mounted on the kart, I think that'll help