Removing this pipe should be the easiest part of the PS replacement, yet it seems to be the most troublesome for most people. That red ring is a compression fitting, and is designed to hold the pipe in. The harder you pull on the pipe, the tighter it will grip the pipe, so don't keep pulling harder, and definitely don't try to pry it out. That 2001 video is dead wrong and he just got lucky the second time around. You need to relieve the compression by pushing the ring toward the pump before pulling out the pipe. Then the pipe will slide out just like any other well-lubed male/female coupling
You can either use 2 plastic spatulas (as described in the service manual) in which case you will need 3 hands, or use a tool like the one I linked to above. Believe me, it will be the best $2 investment you've made. You don't need to make one out of metal, plastic works fine and won't destroy your pipe or fitting. Just remember, if you pull and there is resistance, don't keep pulling or it will just get tighter.
In your case, it looks like you tried to pry out the compression ring from the pump
? The red ring should stay with the pump and only the pipe slides out. Putting it back in is easy as there is no resistance to push the pipe back in. The compression fitting only works one way. I don't think you can buy the fitting separately. You will probably have to buy a new lower reservoir if you have any leaks. It also looks like you have mangled the pipe pretty badly so you may want to consider replacing that too.