I wouldn't know a solution to run a .exe server side. I do start a .exe from my Mendix app on the client. I start this executabe with an URL protocol handler.
You could add a web service call to your custom Delphi code that communicates the result back to your Mendix app. This will however always be async.
If you really really want this, and you run the server on premise, and the server is a Windows server you can start an executable from a Java-action
Process process = new ProcessBuilder(
"C:\\PathToExe\\MyExe.exe","param1","param2").start();
You can never run this in any cloud. You probably need to open up some security holes in Java, which allow unwanted actions on your server.
If you are allowed to run an exe on the server you could try to use this piece of java
Process process = new ProcessBuilder("C:\\PathToExe\\MyExe.exe").start();
InputStream is = process.getInputStream();
InputStreamReader isr = new InputStreamReader(is);
BufferedReader br = new BufferedReader(isr);
String line;
System.out.printf("Output of running %s is:", Arrays.toString(args));
while ((line = br.readLine()) != null) {
System.out.println(line);
}