YSK: You don't need Gmail to create a Google account
Why YSK: A Google account is not the same as a Gmail account, and you don't need to create a new Gmail email account to have a Google account.
I've spoken to many different people who equate a Google account to a Gmail account. This is not the case. Unfortunately, this leads to many new Gmail accounts being created, solely because they think that they need to have a Gmail in order to access other Google services.
Here's the gist:
A Google account gives you access to Google services like Sheets, Docs, Calendar, Drive, Photos, Gmail, YouTube, etc.
A Gmail account is an email service account with Google. When you create a Gmail, you also create a Google account by default.
However, the reverse is not true. If you create a Google account (with a non-Gmail email address), it does not automatically give you a Gmail account.
If you already have an email account with another provider, you can use that as your Google account.
For example: Let's say your email is jane@example.com. Rather than creating jane@gmail.com, you can opt to create a Google account with jane@example.com and avoid creating an account for Gmail.
Unfortunately, Google tries to get you to create a Gmail account during the process of creating a Google account. (see image).
It's important to differentiate this and prevent people from registering new Gmail accounts unnecessarily.
So is this why I’m able to receive new emails from the Google Group I joined with my non-Gmail account, but not actually access the Google group to see past messages to the group?
Sounds like it. It happens with other Google services too. Someone could share a GDoc to your non-Gmail email, but if that non-Gmail email isn't a Google account, then you won't be able to access the doc/comments/whatever else (depending on the doc permissions, of course).