A compatible Atmega8 QFP32 to DIP28 adapter would be expected to have 28 pins.
The shown adapter has 32 pins, I guess it has a 1:1 pin wiring (you may have already checked). In this case, the adapter can be only used with a specific programmer if the programmer is prepared for performing the required pin mapping. You should check the documentation.
- - - Updated - - -
I found that newer TL866 II supports ATmega QFP32 programming but TL866 doesn't. It would require a special wired adapter according to DIP28 pin mapping. See the information for TL866 II below.
View attachment 150603