Hello again,
just to refine my bug report, Speccy canNOT even be run by a Windows User the standard way (e. g. icon double click) - the system returns a missing Administrator privileges prompt (see attached screenshot), which does NOT even ask for the Aministrator's password (only simply rejects the attempt).
Speccy thus can only be run using the "Run as administrator" Windows' option - and, as written before, then needs to be minimized to Tray manually.
Hope this helps the developers debug otherwise very nice and useful Speccy. Thanks for it, by the way.
Kind regards.
P. S. Interestingly, for the Administrator Speccy now minimizes to Tray automatically - w/o any settings changes done. Don't know, what happened (it doesn't seem to have been updated http://www.piriform.com/speccy/version-history).