This is known as Nominalstil. The noun phrase* in front of the verb zählt can be compared to a sentence like the following, where 1 is an object (wen?), 2 is an adverbial of manner (wie?) and 3 is an adverbial of place (wo?).
Man muß [alle Geschäftsführer einer GmbH]1 [mit Namen]2 [in der eMail-Signatur]3 angeben.
Assuming by cases you meant noun cases: einer GmbH is genitive (because it is an attribute of a noun), Namen is dative (because of mit), der eMail-Signatur is dative (because the preposition is in and the question is where?).
* Wikipedia has an article on noun phrases. The idea is that nouns can be expanded:
Untersuchung
die Untersuchung
die geforderte Untersuchung
die geforderte Untersuchung des Betriebs
die geforderte Untersuchung des Betriebs auf Salmonellen
In your example, the noun phrases in front of the verb is
die Angabe aller Geschäftsführer einer GmbH mit Namen in der eMail-Signatur