FFmpeg says that it can use `drm` hwaccel method, so this is not caused by it.
Found an interesting condition inside Kodi settings XML definitions:
<setting id="videoplayer.useprimedecoder" type="boolean" label="13430" help="36172">
<requirement>HAS_GLES</requirement>
<visible>false</visible>
<level>2</level>
<default>false</default>
<control type="toggle" />
</setting>
It looks like in order to be able to use DRM PRIME, Kodi must be compiled with GLES support.
#ifdef HAS_GLES
m_simpleConditions.insert("has_gles");
#endif
However, the version of Kodi from the official XBMC PPA was not.
So basically, yes, Kodi must be recopiled to get HW acceleration to work.
Update:
Actually, it turns out that Team Kodi don't provide ARM builds in the PPA, all this time I was using the Debian build (lol).