It is common for strong chess players to have chess games in memory. Is this because it helps to memorize chess games?
I would switch the cause and effect. Strong players have many games memorized because chess memory improves with strength, not because the memorization made them strong. I am not saying that memorizing games is useless but I think that there are more efficient ways to improve.
I am not sure if memorizing games helps as much as studying games. If you want to learn how masters execute long-term plans or how tactics support strategies or how strategies yield tactical opportunities - then you want to study games (or sequences of moves). Having memorized games (and positions) can help very much when it comes to teaching chess. When I demonstrate the Opera Game to my son I want the experience to be seamless - not interrupted by me looking up the next move.
Many people think that chess is a sport of memorizing moves and tactics, because they see people do the same moves over and over and over in many games, from openings to even end game tactics.
However it's not because we memorized the games, not by any means. For example until today I have not memorized even one single game in my life, yet I have beaten masters before. But if you showed me a game where a certain tactic is played I would still know it even if I didn't memorize the game itself.
In short, memorizing is something that happens to a chess player when he plays a lot, you will intuitively know moves without having to think, you will know what will lead to where in many scenarios (as long as you don't hit the 2000+ bracket)... And the main reason is because you had trial and error and learned these same tactics they are using by heart.
^^^^ That was the main answer, if you wish for more in depth, please read further :)
In essence, memorizing a chess game does not make you better, nor does it NOT make you better. if you memorize a chess game it is not because you want to use it in an actual game, rather it should be memorized so you can learn from it.
Memorizing anything besides openings in chess will mostly end up in failure... In tournaments you will not be thinking about what you last memorized or whether or not that certain tactic (whatever it may be) will work according to the piece placement that was in the game... That will never help you in a real chess match.
However, they will help you when you reach a high level of chess and already know a good amount of tactics, strategies, sacrifices and of course end games. They will truly serve you well then, however until you reach that level I advise you to focus on learning the heart of the game.
By that I mean start off by learning some basic openings that will help you learn chess in all kinds of positions (usually I advise people with the Italian Game and French Defense) and learn the basic tactics and value of pieces and when to trade a good piece for a bad piece etc... There are many things for you to learn even until today Masters learn the game. So don't be surprised if there's a lot out there :)