After reading the article I still don't understand what the world looked like to him. What does it mean by backwards here?
I have no idea what "M looked at his wristwatch from any direction to check the time" is supposed to mean, but it seems to be a red herring.
In my understanding the meaning is « M can check the time from any direction ». As you and me of course, but usually our spacial memory retrieve the time from the needles orientation (no digit watch in WW2) so we use to always check the time in the same position (12 upward). As M can’t rely on the position of what he see, he probably just « read » the watch numbers all the times (no pun).
Most unusual of all, though, Patient M saw everything as though it had been inverted. Highlighting the case in his book, Cerebral Dynamics, Rodríguez-Leal revealed how the war veteran “found his abnormalities strange when, for example, he saw men working upside down on a scaffold.”
El paciente M: el hombre que empezó a ver el mundo al revés tras un tiro en la cabeza en la Guerra Civil
The real test as to whether the brain learns to flip the image would be if the goggle-user could read upside-down text after using the goggles for a few weeks, without having read text during that time.
[0] inverted.