If you follow the video, no risk at all really, all the test does is complete a circuit which in effect turns it on, same as happens when you press the power button on the motherboard. This is a standard test used to test PSUs for decades.
The Corsair CX was probably s step up from what you had and is not a piece of junk by any means but it is not up to the standards you will usually find on their more expensive units. It wasn't a bad choice. If it has died then it was probably simply defective. But it might not even be the PSU. Could be something else entirely, but we need to start troubleshooting somewhere and this is the easiest first step and the most likely cause, that's why it is step one.
If you prefer you could examine the motherboard for burn marks or other damage first, that would be step 2. Buy you should take the MB out of the case to do that properly and that is a lot of work to do if it turns out to have been the PSU. You can do the PSU test in the case but you must unhook ALL power connections to the board and components.