If you think an FPGA is not inherently and necessarily a state machine, no matter how it is programmed (provided power and clock are in specified bounds), that only means you don't know what a state machine is. All clocked digital devices are state machines, and can never be anything other than state machines.
(There is an argument to be made that an FPGA is, itself, an ASIC: an IC whose Specific Application is to be an FPGA. But such an argument would be transparent sophistry.)