Wired only DSL modems compatable in 2021? [Answered]

The DM200 is a gateway that works on both Legacy DSL (a role for which AT&T still allows it to be used) and ADSL2+ (for which it won't work... it doesn't have the AT&T certificate and won't authenticate). 

It will not work with your circuit.  You are right, there is a difference between "officially support" and "will work."  In this case, AT&T requires the use of Gateways that have their authentication certificate.  No certificate, it will not work.  You cannot avoid the Equipment charge unless you (a) go back in time and purchase a gateway 7 years ago and get grandfathered into the plan with the last few gateways that still work, or (b) talk them into giving you a promotion where they discount the price of the Gateway.

Whether or not the Gateway has Wi-Fi is irrelevant to the discussion.  If you don't want Wi-Fi, you may turn it off.

Brand and model number?

I currently have the BGW210 hooked up, but want to purchase an older NON-WIFI AT&T Modem. Not sure which one. That would have been my next question. If I can indeed use a wired only modem, which one would people recommend? Like the last of the Mohicans of the wired modems that still performs decent. I'm no power user. Just watch videos, movies, maybe play a few offline games occasionally.

Your tag is hilarious BTW. 
That's my fall back retirement plan. 
Way more fun than an old folks home. 
And who knows, I may get away with it. 

All of the devices that AT&T supports for VDSL2/ADSL2+ connections (which is what you have) have built-in Wi-Fi.  In addition, AT&T no longer supports any device that a customer can buy on the open market for their services, nor do they sell the devices that have their required authentication certificate.

I don't need "support" persay. I just need it to work.  
For instance, the Netgear DM200 DSL VDSL and D-Link ADSL2+ ethernet modem (DSL-520B) worked with AT&T DSL in late 2020 according to many reviews and forums. 

So, are you saying the DM200 will NOT work with Legacy DSL because of certs? 
OK, so my options are: 
1. Build a time machine and travel back to 2005. But wait...I would have lost that modem in a 2015 wildfire anyway, so I'd have to travel back to 2015 and warn myself somehow to protect my modem. 
2. Turn off my wifi. 

2 sounds way easier. :D