So, after more or less successful update from 8.1 to 10, where Asus Xonar Essence STX worked perfectly fine up to this date, it stopped working on 2015/08/18 with no notice. Trying to install using available 8.1 driver reports "not supported platform".
This is a solution that... sometimes works:
http://maxedtech.com/asus-xonar-unified-drivers/"Driver should be available in October"?