All Quiet on the Western Front was published in November 1928 in Germany.
'Wireless Telegraphy', which is the transmission of signals (not the sound of a voice), was still only in the hands of Governments, not the general public or commercial companies.
The transmission of sound (radiotelephony) began to displace wireless telegraphy by the 1920s for many applications, making possible radio broadcasting. Wireless telegraphy continued to be used for private person-to-person business, governmental, and military communication, such as telegrams and diplomatic communications, and evolved into radioteletype networks.
'Wireless-men' would have referred to Government employees engaged in Signals Intelligence. (Our equivalent would be GCHQ in the UK or the NSA in the USA.)
From the mid-twenties, German Military Intelligence Abwehr began intercepting and cryptanalyzing diplomatic traffic. Under Hermann Göring, the Nazi Research Bureau (Forschungsamt or “FA”) had units for intercepting domestic and international communications.