[JdeBP]

… and no, since neither the enciphering nor the deciphering do a 1:1 mapping for all possible input code points.

[amenhotep]

That's not a requirement. Pigpen is a substitution cipher.

[JdeBP]

You will find that the pigpen cipher has a 1:1 mapping between its input alphabet and its output alphabet, and that a 1:1 mapping is a necessity for full invertibility.