This might be a false memory, but in the 90s could you not get a pocket sized fixture card? Just a folded over bit of card with all the games and space to fill in the scores?
The answer to that is not to do nothing. Put sign up links where people can find them, have opt-in checkboxes on the shop, lotto, ticket sales, etc. At least mention on the website that the mailing list exists!
Interesting. In that case they need to expand their mailing list and show people how to sign up. For example, I play the lotto every week and get an email about that, but have never heard of this other email.
They could start by maintaining an email list of people who have contacted the club, bought from the club shop or bought tickets and send them weekly emails with details of fixtures (with link to buy tickets), club news and a divisional roundup. Nothing too complicated, but puts the information in front of potentially interested people efficiently.
It's going to be a long season if we get folk looking to say I told you so after every good game and other folk doing the same after every poor performance.