I think you might be misinterpreting the API Terms of Service, or if not then there is some ambiguity in the terms themselves.
Twitch user data for users not created by your application may be stored for no more than twenty-four (24) hours.
The keywords that I believe you are missing I’ve highlighted. Essentially, if the user has not authenticated to your website using Twitch, then you cannot store their data for more than 24 hours.