Hi Orangecat,
A great question!
To give you a short answer; yes, you can say both. The first example (re; "He would have really wanted…") you are using a past modal + perfect infinitive.
The “would have” makes the answer shows the present feelings about the past hypothetical event. For example ,“I would have liked to be a singer”. In my example, I still want to be a singer, but I am not, yet the dream of being a singer is from the past.
The present infinitive (re “to have seen this”) in the sentence is used to show what might have happened. In this case, it is the person seeing the thing.
Together they are showing the hypothetical outcome of situation that never happened and their feelings towards it. A very difficult bit of grammar to understand!
You can also say “He would have really wanted to see this” but you are taking out the present infinitive. In principle, you are saying the same thing, you are just emphasising the present feelings rather than the past outcome. However, overall, no one would think any different of it.
One last comment is that, I am assuming that the YouTube video said “loved” not “love” because it doesn’t make sense to put the bare infinitive there…
It is very complicated so if you have any other questions then please feel free to contact me www.italki.com/maddie.
Good luck!