It makes sense now that you describe it as a dialog box instead of a "magic app that doesn't show up in the cmd-tab switcher", which is how I thought of it before. If it were any other app and I wanted to find the dialog again, I would cmd-tab to the app. I guess the problem is that whatever app it belongs to (Dock.app?) has no place in the cmd-tab switcher.
(on my Mojave machine, it does stay open when I move away from it, when I cmd-tab to something else and then a third something else, "About this Mac" is still visible.)
(on my Mojave machine, it does stay open when I move away from it, when I cmd-tab to something else and then a third something else, "About this Mac" is still visible.)