Not sure if I understand completely what you need, but the button’s functionality is applicable with just the URL that is displayed after you have clicked it. So you can copy and paste the URL to start Kodi (http://max2play/plugins/max2play_settings/controller/Xbmc.php?action=start&downloadurl=http%3A%2F%2Fsteinerdatenbank.de%2Fsoftware%2Fkodi-15.tar.gz&addonurl=&addonbox=) and integrate it into any application you want in your local network. You can, for example, add a bookmark on your smartphone or tablet for this link to have it switch with one touch on your device. You can of course, also integrate into a script for your TV.
I hope this solves your problem.