Probably zero impact, considering all the cryptography you'll ever need has already been implemented securely in many libraries (openssl, bouncycastle, etc...) and you almost never (and should never) implement it yourself. But learning about cryptography certainly is worth it (but until you actually know what you're doing you shouldn't use it in your commercial projects).

Furthermore cryptography in general is not a very useful tool when it comes to preventing cheating etc... Cryptography solves these problems:
- confidentiality (controlling who can read what you wrote)
- integrity (making sure a given message arrives intact to some destination)
- authenticity (knowing who produced/sent data)

In general these are not the problems you want to solve when making games.

Cryptography in gameplay? You mean as in crypto minigames or something? Can you give an example?

puzzle mechanics.

Then sure I guess, but it has to be kept simple (cryptography understandable by average human beings, e.g. back to caesar's code or vigenere level stuff). Perhaps this should be moved to Game Design if it is going to be about how to integrate cryptographic concepts into game mechanics as puzzles or problem solving etc.. you will get more responses I think.