How the device (that is off) decide how to publish itself for USB: "MediaTek PreLoader USB VCOM port" or "MediaTek USB Port" device? How the mobile phone (that is off) informs the Windows PC (with installed drivers "MediaTek PreLoader USB VCOM port" and "MediaTek USB Port") how to identify itself: as device 
- "MediaTek PreLoader USB VCOM port" or as
- "MediaTek USB Port"? 

When I plug the phone to USB, Windows PC connect it sometime through "preloader USB", sometimes through "just USB" ports, sometimes both  in sequence  (I see it from WMI events). I don’t see any pattern related to "time after next attempt" or "volume buttons pressed".

P.S This is "the phone off" state when battery is inside. What are correct names for those states (battery "in" and "outside")? When battery is extracted - device is not recognized as USB device by PC.
I can't see the question here ? 

Are you asking what the driver is for ?   

Please have a look at this video to understand what the preloader is, MTK Backup &amp; Restore  

The Mediatek Preloader is used for flashing new image's to your device.  

Their is two different boot loaders on Mediatek device's.. 


MTK DA USB - For flashing the Preloader   
MTK Preloader  - For flashing all other image's     


How does it register as a device while it's off ?
This is so you can fix your device when it won't even turn on, it need's to be before the boot of your system.  

I hope i somehow answered the question here.