No, there is no way to have variables automatically updated when other variables change.
What you can do instead is create a custom keyword that changes all the variables at once.
*** Keywords ***
| Reset app directory
| | [Arguments] | ${path}
| | Set global variable | ${APP_INSTALL_DIR} | ${path}
| | Set global variable | ${APP_LAUNCH_PATH} | ${APP_INSTALL_DIR}\\app.exe