is this game just memorization?
How many puzzles would you recommend doing as a beginner to the game? Should this be a main focus, or would it be better to just play more games?

Pattern recognition is FAR more important than mere memorization of moves.
There are certain checkmating patterns called "model mates" that are very useful to learn because they can become new "tools in your toolbox", just like Knight forks or back-rank checkmates are.
An example:
Greco's mate is characterized by the enemy King being held in the corner by a Bishop while your Queen administers the checkmate along the file.

Let me know if you are interested in seeing a few more of those mating patterns... Lolli mates, Smothered mate, Legal's mate, etc.

That 2nd one was pretty nifty.
Practice and board vision is essential. Until you can see the entire board and not just the 16 squares of interest, you are going to have issues.
That 2nd one was pretty nifty.
Practice and board vision is essential. Until you can see the entire board and not just the 16 squares of interest, you are going to have issues.
That, and you have to work on the cognitive biases that your brain is susceptible to, as explained by coaches such as Dr. Can & NM Dan Heisman.

At the higher level is mostly memorization of theory and previous games for me
you're not there yet, don't worry.

To get good at almost anything, you need to remember things. For example, if you're an engineer and forget the right formula, or if you're a wielder and forget which tool to use in which order.... And in chess, you need to remember things like your mistakes, openings, tactical patterns, positional patterns, and more. So you could argue that chess is mostly memorization.
But thankfully, chess is a logical game. Principles can be deduced if you know the reasoning, and you can apply them in many situations. Calculation is something to be trained, not memorized. And patterns are ingrained through repetition, not rote memorization.
While openings can improve your results, they won't improve your level play (someone who plays openings like a grandmaster, but the rest of the game like an 800, will probably be rated 900-1200) - it may help you overcome a small rating hurdle, but at the end of the day, if you wish to get better, you have to improve on actually playing the game, which isn't about memorization.
Hopefully, what I said makes sense.