I was able to figure out my issue. The password I was using was 32 characters long. Which the website is fine with, the updater when initially logging in worked, but when trying to patch the updater, it just closed and never reopened and updated. I changed my password to have less than 14 characters, and the updater no longer crashes and it updates successfully and I can now launch the game.
So two takeaways from this experience:
Do not have special characters in your password (I have seen this mentioned multiple places)
Keep your password length on the shorter side.