I have the smaller Domino (500) and have used it on several projects. Not an expert by any stretch.
If I were making the frame and panel back as your SIL did I would have made up all the rail and style parts with stub tenons to fill the grooves in the intersecting piece. Then I would have plunged Domino mortices right through the Stub tenons and slots. These can be as thin as the slots or thicker. Might look a little brutal, but once it's assembled it will do it's job and no one will see.
Once you have the Domino, like many other tools you will think of many uses for it. An example is it's a wonderful thing for make slots around the inside of a table rail to accommodate the clips or buttons that will hold the top on. Literally seconds to do.
As to TomD's speculation that "real" M&T joints are stronger, I don't know. I suspect he is correct, but I haven't seen any research that proves it. I suspect a perfectly cut traditional M&T is stronger than a Casually done Domino, but can't prove it. Another aspect is you can install fifty Domino style mortices in the time it would take you to do five or ten traditional ones. I am more inclined to "throw in" a few dominos than to do a few hand cut ones when in doubt they are necessary.
One of the things that holds me back on Dominos is the cost of the individual dominoes. (Yes I am cheap) I have largely solved that problem. At an auction I bought a pallet of birch or maple sticks that are 3/8" by 7/8" by 16" long. I have abut a thousand of them. The narrow edge is rounded. Unfortunately, 10mm,s is about a 1/100" to big. but if you reduce these stick to 8mm, taking a little off each side, they fit the 8mm Domino mortice perfectly. I made up several hundred in two lengths and now have what might be a lifetime supply.
So, Bill, or anyone else is listening, I will send you a gift package of the strips (unmodified) and you can make up your own and use them with reckless abandon, all for a small appropriate donation to Wood Central. The Domino is a lot more fun when you don't care what the Dominos cost. Also, I sanded a few of mine down to a loose fit and have them for making quick dry assemblies to see what it looks like before committing to glue. (Actually they were made out of a stick or two I planed just a little too thin.)