Still using BitDefender engine. You should be able to find the files in "Common Files" folder in program files.As soon as I saw the architecture on your screenshot, I realised it's gone. Maybe BullGuard has switched to someone else...I will investigate rn.
BullGuard uses only the BitDefender core engine + defs along with a rootkit scan driver and the BullGuard cloud.
Real time scanning processes and drivers are self developed, including the webfilter (though, I speculate the webfilter may still use BD database but the certificate and https scanning etc. are self developed).
BullGuard is not a direct rebrand of BitDefender as in there are a lot of self developed technologies (kind of like Emsisoft).