Hi Marijke
Excuse my rambling, I'm just thinking out loud :)
It's very interesting to see the code - was it you that highlighted the Print Execution function definition? It's only a fraction of what is required.
There is a lot of code in there, much of which can be reverse engineered into App Inventor code and some of which can be ignored - for example, extracting the tape width sizes from available .lea files can be done with VBA in Excel as a one-off and the results used to define permanent AI Lists. However, launching (Activity Starter) the Epson Label Editor for Android might well be necessary for anything graphical. Portions of the code glean data from the Excel workbook. For text based labels you would have your own "label arrangement screen" which might be as simple as two or three Text Boxes.
A huge amount of work (though if you enjoy a challenge and are not in a race against time, should be a lot of fun), there is a gotcha in that the labels (CSV) are using UTF-16 and App Inventor uses UTF-8 - chalk and cheese! This means you would need a procedure that 'converts' your AI UTF-8 Strings to UTF-16 and that would be at byte level. An AI extension would be the way to go - Android Studio does do UTF-16, it's the native encoding of Java.
Conclusion: Doable, with copious amounts of coffee a necessity, but there would have to be a solid reason to do it (other than the joy of coding) given the challenge, time consumed and the probable lack of commercial viability, especially given the fact that Epson already provide an Android app.