Historically, most applications supporting multiple files would have used MDI interface, which is perfectly happy having just a window with no documents open (the equivalent of a Mac app with no windows open). Normally, this window has nothing but a menu bar, and perhaps a toolbar.

But for single-document applications, what I do (on Windows, running Cygwin), is roughly this:

for f in *.your-file-ext; do cygstart --wait "$f"; done

That'll iterate through each of the files in sequence, opening them up in the application registered for that file type, and wait until the application is closed for each file.

If some action is required, I might stick a 'read' in to that ad-hoc script.

(Disclaimer: I contributed the --wait flag to cygstart for just this kind of task.)