Torque is transferred from the shaft to the bevel gear through a key, which is not related to the thrust bearing.
When bevel gears turn, they try to slide down the shafts to get away from each other. It is important to design around this load to reduce friction and to keep the gears from pushing on things that are delicate.
Thrust bearings are used to reduce friction between two faces that can be rotating at different speeds that are being pushed together. If there wasn't a thrust bearing, and you pushed these faces together (like from the thrust loads from the bevel gears), friction would slow them down, like a brake on a bike. Unlike normal ball bearings, which deal with loads on the curved inner and outer races, thrust bearings deal with loads in the direction of the shaft on the flat surfaces. The rolling balls in the middle let the two washers rotate at different speeds, even when they are being pushed together with a lot of force. They're similar to bearings on lazy susans and microwave oven turntables; they still spin freely when you push down very hard on them.
http://en.wikipedia.org/wiki/Thrust_..._din711_ex.png
You can see another example of thrust bearings in 1640's module rotation. They use a thrust bearing between the top rotating surface of the swerve module and the fixed frame of the robot. There is the weight of the robot pushing down on the top of the swerve module, and the thrust bearing here allows the module to turn very smoothly and with low friction even though there is a ton of force pushing the two together.
The purpose of the thrust bearings in the picture you see are to deal with the thrust load of the bevel gear. If there were no thrust bearings, the bevel gear would sit against the inner race of the normal 3/8" bearing in the module. If moderate thrust loads are applied to the inner race of the bearing, the bearing can get destroyed, so they want to transfer this load to something else, like the outer race of the bearing, which, through its flange, transfers it to the side of the module. In order to do this, they have to deal with the gear, which is spinning, and the outer race of the bearing, which isn't, so they use a thrust bearing.
Teams have used swerve without thrust bearings here, but I have no idea if it worked well for them or not. The thrust bearings are cheap ($2.47), so it makes sense to put them in.