"Vera is the café's administrator."
Translation:Вера — администратор кафе.
You are indeed correct in that we use the genitive case here. However, кафе like many other imported words (кофе, такси, и так далее) is what we call an indeclinable noun, therefore the word doesn't change regardless of its case.
Another quick note - The genitive ending for neuter nouns ending in е, such as море, is я. You can take a look here for all of them. http://33.media.tumblr.com/5127b0b1aed2c5fd501d5ecc3a4747f3/tumblr_inline_mzgehrXN2T1qgkwq1.png
[ Ка-фе́ ] is a Noun, not an Adjective. The [ кафе администратор ] phrase puts [ кафе ] in the context to perform as an adjective, modifying [ администратор ], what kind of administrator.
[ администратор кафе ] ‧ [ Administrator of the Café - literal grammar ] works because [ Ка-фе́ ] is able to function as the Noun that it is grammatically. Due to [ Ка-фе́ ]'s indeclinability, it is less obvious that [ администратор кафе ] has put [ Ка-фе́ ] in the Genitive Case.
[ Ка-фе́ ] is a borrowed word from French [ Café ] which borrowed from Arabic [ قهوة ‧ qahwa ]. Besides being indeclinable, I do not find a Russian [ Ка-фе́ ] adjective form, ala [ Ка-фе́ш-кий - just a made up word ]. A similar ancient Russian native term may likely have an associated adjective with the noun word.
[ Ка-фе́ш-ка ] is a declinable diminutive derived from [ Ка-фе́ ] but I do not find an Adjective form for it either. ‧ ru.wiktionary.org/wiki/кафешка ‧