You will want to go to the wall controls and find out what model they are. You may have to remove one from the wall. I'm not 100% sure, but I believe that the wall plate with the 25 pin connection is their proprietary setup that is designed specifically to work with a controller unit. It's COMPLETELY insane that you would move into a new place and they would have deinstalled that piece as it is required to make all the wall plates work. You can't use the controller without the wall controls and you can't use the wall controls without the controller. I would never sell my home and take a piece required for core functionality.
That said!
Nuvo units are on eBay. They aren't as slick as what you linked to, but I'm thinking that what you have won't work with anything but a legacy product. It is possible that they wired all the keypads with network cabling and that your speakers are run to the same location. In which case, it may be possible to dump the old equipment and upgrade everything to the new gear.
But, if that's the plan, it may be better to look at other solutions. That is, maybe putting Sonos everywhere and running it all from your phone.
I'm not a fan of running everything from my phone. I like having a keypad in the room.
If I were you, I would pull the wall unit, find out the compatibility with legacy Nuvo gear, maybe give them a call, then get a replacement unit that is compatible from eBay or perhaps even new. They have software you can use right on their website, but it will take some work to get it all going and there will likely NOT be any phone/mobile control possible. As common as it is these days, 5-10 years ago, most homes didn't have any mobile control and the products made didn't offer it. Now it's common, but legacy products don't support it. Nuvo for sure has this headache on older stuff. I'm looking to lay a simple Crestron system in to run a an older Nuvo system from someone's phone. It's an Essentia system from them. I'll let you know how it goes.