The penalty shootout is a round and the chances are 50/50 and luck in my opinion is one of the important factors, apart from mentality. Real Madrid successfully won on penalties, from what I saw they had prepared for this, and we also need to know that they were very effective when attacking in normal time so Manchester City couldn't beat them.
Paris Saint Germain was just unlucky in my opinion, because if I look at the opportunities they had when facing Borussia Dortmund in the second leg, they had a lot of opportunities, but those opportunities could only touch the crossbar. In my opinion, luck is on Borussia Dortmund's side in this match.
Mental is needed when players are given the opportunity to execute penalties and if one of the players is not calm, it is likely that a goal will not occur. In addition, luck is also a determining factor because penalties have a chance as you said. But we must admit that Real Madrid are used to facing pressure like this so they will be much more prepared and able to come out as winners. That's why the Champions League is different because it takes mentality and experience to face pressure in every match.
Statistically PSG is indeed superior to Dortmund, but they are able to take advantage of even the smallest opportunities. In both away and home games PSG had many chances to score but they could not make the most of their chances to score. Dortmund were able to play more effectively by making the most of their few chances to score.