The SOIC16 25FL016A should be supported too since it is only the pinout different. So, the adapter is need for this chip to for this chip.
Currently there is no direct adapter for it. But you can use jump wire to map the pin to 8 pin chip pinout. The adapter you can use is ADP-028.
You need ADP-028, ADP-067 and CPT-022. Put the chip in ADP-028, put the ADP-067 on the programmer, then use CPT-022 to map the SOIC16 pin into SOIC8 pinout. In software should select 25FL016A soic8.