According to the documentation the gpgme_op_encrypt method of GPGME is able to perform symmetric encryption tasks:
gpgme_op_encrypt (gpgme_ctx_t ctx, gpgme_key_t recp[], gpgme_encrypt_flags_t flags, gpgme_data_t plain, gpgme_data_t cipher)
If recp is NULL, symmetric rather than public key encryption is performed. Symmetrically encrypted cipher text can be deciphered with gpgme_op_decrypt. Note that in this case the crypto backend needs to retrieve a passphrase from the user. Symmetric encryption is currently only supported for the OpenPGP crypto backend.
But where does the key used for the symmetric encryption come from? Is it somehow possible to fetch this key and transfer it to another device (where I would like to decrypt the text) ?
The session key for symmetric encryption is derived from a passphrase, which will be queried from the user through one of the pinentry methods. Specifically highlighting a part of the text you already quoted:
If recp is NULL, symmetric rather than public key encryption is performed. Symmetrically encrypted cipher text can be deciphered with gpgme_op_decrypt. Note that in this case the crypto backend needs to retrieve a passphrase from the user. Symmetric encryption is currently only supported for the OpenPGP crypto backend.
I'm not aware you can extract the session key through GPGME, but you don't really need to: all you need to know at the other end is the passphrase used, and the session key can be derived again. You could of course also reimplement the string-to-key-function used for OpenPGP.