As noted, the referenced script is only written to handle being double-clicked on. There's nothing in there that tells it what to do with dropped files, so it just ignores them.
Additionally, as suggested, this would be relatively easy to rewrite as a shortcut/Quick Action.
But if you really want a droplet, it's pretty simple to change the script to accept opened files.
The original script is just one list of commands to run.
This revised script puts all of that heavy-lifting into a handler (I called doIt, but it can be anything you like), and adds two handlers - one for when the app is launched, and one for when it has files dropped on it. Both of these handlers simply identify the file (either by referencing what was dropped, or by asking the user for a file) and then passes that to the doIt() handler.
Untested, but it's pretty straightforward:
-- this gets run when the app is launched directly:
on run
set thisPDF to POSIX path of (choose file of type "com.adobe.pdf" default location (path to desktop) without invisibles) as text
doit(thisPDF)
end run
-- this gets run when files are dropped on the app:
on open (theFiles)
repeat with each_file in theFiles
doit(each_file)
end repeat
end open
-- this is the pre-existing script with a file passed in based on the above:
on doit(theFile)
set basename to (NSString's stringWithString:thisPDF)'s stringByDeletingPathExtension()
set basename_sfx to basename's stringByAppendingString:SUFFIX
set outPDF to basename_sfx's stringByAppendingPathExtension:"pdf"
set outURL to NSURL's fileURLWithPath:outPDF
set inURL to NSURL's fileURLWithPath:thisPDF
set pdf to PDFDocument's alloc()'s initWithURL:inURL
set {{x, y}, {w, h}} to (pdf's pageAtIndex:0)'s boundsForBox:(current application's kPDFDisplayBoxMediaBox)
set pdict to (NSDictionary's dictionaryWithObject:outURL forKey:(current application's NSPrintJobSavingURL))'s mutableCopy()
pdict's setObject:(current application's NSPrintSaveJob) forKey:(current application's NSPrintJobDisposition)
pdict's setObject:outURL forKey:(current application's NSPrintJobSavingURL)
set printInfo to NSPrintInfo's alloc()'s initWithDictionary:pdict
printInfo's setVerticalPagination:(current application's NSPrintingPaginationModeAutomatic)
printInfo's setJobDisposition:(current application's NSPrintSaveJob)
printInfo's setTopMargin:36.0
printInfo's setBottomMargin:36.0
printInfo's setLeftMargin:36.0
printInfo's setRightMargin:36.0
printInfo's setPaperSize:(current application's NSMakeSize(w, h))
set printOp to pdf's printOperationForPrintInfo:printInfo scalingMode:0 autoRotate:false
printOp's setShowsPrintPanel:false
printOp's setShowsProgressPanel:false
printOp's runOperation()
return
end doit
You'll need to play the same code signing shenanigans again with the new version of the script