Sorry, I am not ready for philosophical discussion. We can take definition from Wikipedia: https://en.m.wikipedia.org/wiki/Computer_programming Programming involves code execution on computer. There is no computer in FPGA.
Technically FPGA is a piece of memory. The functionality of the FPGA device depends how the bits in this memory are set. Size of this memory is constant This information is not public, brave hackers are working hard to reverse engineer this. You can make a CPU in FPGA, no way for the opposite performance wise. Complex simulation with couple 4k resolution pictures takes days.
Edit: the people here are decent enough to start a discussion.
There is a term “variable program” in your link. When you add peripherals to the chip on the printed circuit board it looses flexibility very fast. The whole system is made to very specific task. But yes, you convinced me that FPGA might be treated as a computer in an extreme case.
FPGA accepts "variable program"s. What you are talking about are peripherals. A CPU with certain peripherals can also be completely inflexible. That is completely outside the scope of what a CPU or an FPGA are though.