Now I'm not at work, or on my phone, I might be able to get my links right!
I think this thread will be useful to you:
http://www.xt660.com/showthread.php?t=20512 (Posted by the same chap who made the video you saw.)
The socket required is 37mm (according to the above thread).
It is also worth noting that the problem with crank nuts coming loose appears to be down to Yamaha specifying a torque setting on the low side. Service manuals quoted 80Nm for the nut, but dealers who have rectified this issue have been torquing the nut to 110/120Nm.
I reckon you'll get away with tightening it to 110Nm and reusing the tab washer (assuming there's nothing else amiss).