Unless something has changed that I don't know about, cruises are treated differently by Mexico and the passport requirements you found are for other methods of entering Mexico. As a hypothetical (a really big hypothetical!), if I arrived in Cozumel on my private yacht they'd want to see my passport.
Mexico is a signatory of the WHTI which allows for the closed-loop exemption. Thousands of people are taking cruises to Mexico every week with just birth certificates and a photo ID (photo ID for adults). Just make sure they are the original or a certified government copy and not photocopies of those birth certificates you made at the local Staples.
As always, you'll want to verify what I said with your travel agent or the cruise line if you booked with them because Cruisemates offers no guarantee that information provided here is accurate. But I suspect we'd have heard about any changes of this magnitude.
And also, as you know it is always a good idea to have passports for everyone. You never know if you might have to fly home from another country, and in that case you would need passports.