Actually there are 2 different thermal fuses, the one on your picture is placed near the heater and is meant to cut power to the heater in case it overheats as a safety feature.
Another one is placed after the blower. This video will show it better that I can explain:
https://www.youtube.com/watch?v=leM7XTm7oz8Based on your short video, I don't think it's the problem. The dryer sounds like it's trying to start, but the motor doesn't have enough torque so it promptly overheats and stop.
This could be because the belt is not properly on the pulley and has stuck, or there's something preventing the drum from turning, or the motor bearings have seized, or there's an obstruction in the blower wheel.
Unfortunately for these models, if you remove the belt from the idler pulley and motor pulley, there's a safety switch that will prevent the motor from starting, so you can't check motor by itself.
However, with the front of the unit removed, you can access the blower wheel and turn this one by hand, both with and without the drum belt. It should be rather easy to turn in both situations.
If easy to turn with the belt removed, check if the drum is easy to turn by hand, if yes, it's likely the belt wasn't installed properly. If drum is hard to turn, one of the support rollers might have seized or just isn't placed properly.
If motor is hard to turn even without the drum and there's nothing in the blower wheel, there might be something in the motor blocking it.