The word you heard was not 'dinner' - it was 'diner'. Note that the single 'n' shows that we have a long vowel before it - the word 'diner' is indeed pronounced /ˈdaɪnə/ in standard British English.
A 'diner' can mean one of two things:
- an informal American-style restaurant serving burgers etc, with customers sitting in booths or on stools at the bar
- a person who 'dines' i.e. someone eating a meal. This is the usual term used for restaurant customers. For example, if a restaurant owner says 'We serve a hundred diners per night", they are referring to the number of people who eat there.