If I have only the app.js file of an pre-existing Ext.js application, How do I find out if it is using the modern theme or the classic theme ?
You can´t, you will need the App.json file in order to get all this information, in the application in question, look for the ready2use.json file, Its a classic app using triton, an excerpt:
"id":"0332b510-f907-44a9-97c6-3af68e752bfd",
"toolkit":"classic",
"theme":"theme-triton",
"hash":"b201882bf4eb6467ffa98522c701a54f43b053d2",
"profile":"openmaint",
"resources":{
"path":"openmaint/resources",
"shared":"resources"
}