I did some googling and found a (probably unsupported, but still) Python script:
https://github.com/dillbyrne/es-cec-input
I tried it, it worked, when I started it manually. There's noticeable input-lag, compared to the Kodi implementation, no way that would be useable in a game, but it does the job. Unfortunatelly, I couldn't make it reboot-proof, the @reboot statement in crontab worked, the script was running according to ps, but it did not work. Even more, running it via crontab resulted it in Kodi no longer accepting CEC input either. So I removed it from crontab and am no longer using it.
Is there anyone around here with experience with that or a similar script?
Thanks!