I have now checked little how it checks for certain files:
It actually matches a The Arduino Version in arduino.txt with
known filesizes of the existing files, (it looks by the way that it allows the same version of teensyduino to be reinstalled)
Checking Arduino 1.8.13:
version: "lib/version.txt" version matches
file: "arduino.exe" present
file: "arduino_debug.exe" present
file: "lib/jssc-2.8.0-arduino4.jar" present
java: "lib/pde.jar" object: "processing/app/Base.class" checksum match
java: "lib/pde.jar" object: "processing/app/Editor.class" checksum match
java: "lib/pde.jar" object: "processing/app/SketchController.class" checksum match
java: "lib/arduino-core.jar" object: "processing/app/BaseNoGui.class" checksum match
java: "lib/arduino-core.jar" object: "cc/arduino/Compiler.class" checksum match
java: "lib/arduino-core.jar" object: "processing/app/debug/TargetPlatform.class" checksum match
Found Arduino 1.8.13
The conclusion is that you cannot install Teensyduino on an modified version of arduino ide.