It seems that during dynamic loading of IDEA plugin it doesn't always register its stuff. I've launched IDEA, installed the plugin, became glad it doesn't require IDE restart, then tried to create the project and didn't found corresponding Korge option. Then restarted IDE and Korge appeared in New Project wizard. Disabled the plugin, restarted IDEA, then enabled it and checked New Project again to see no Korge there. Restarted once again, Korge was there.
Am I missing something obvious or should I report this to Github? This is of course minor issue which doesn't prevent one getting started with Korge in any way :)