Many throws in Muay Thai were discarded in the stadiums because they were quite simply too dangerous. Many involved grabbing the lower back and hyper extending the spine. This combined with rotational movement caused many back and lower spinal injuries. I am informed that, to make the sport safer, the throws were analysed and those that were more likely to cause spinal injury were removed.

The clip quite clearly shows the fighter being grabbed in the thoracic region and his back being hyper extended before he is thrown. This is quite simply illegal. If you are judging by the standards of the Thai national stadiums.
If you are to throw an opponant, you have to grab around the upper back and simultaneously drive your opponant backwards. You can also turn and drop them in the grapple, but both techniques should be followed with an effective striking technique to score.

Someone mentioned sweeps, it is my understanding that you can kick the leg away with any part of the front of your shin. Though if you use your calf muscle or the back of your leg to sweep the opponant, this is an illegal move.

I'm seeing Tony Myers today so i'll ask him to respond to this one. As his answers are always more well researched than my own, I also know he has reffed at Lumpini and many of the Kings cup shows recently. So his information should be up to date. This said, what he will say will only be relevant if you are judging the standards by the same criteria as in the stadiums. There are so many differant associations with differant rules, although stating the obvious, this is where the problem lies.