'arena-ish' is a modern English coinage formed by combining 'arena' (ultimately from Latin 'harena') with the adjectival suffix '-ish' (from Old English '-isc', meaning 'having the nature of').

'harena' in Latin ('sandy place') passed into Late Latin and Old French as 'arena' meaning 'sand' or 'place of contest'; Middle English adopted 'arena' to mean 'a place for public spectacles' and in modern English speakers have appended the productive suffix '-ish' to create informal descriptors like 'arena-ish'.

Originally referring to a sandy place or specifically a venue for contests, the root developed the modern sense 'a place for public spectacle'; '-ish' contributes the newer sense 'having the quality of', producing 'resembling an arena' as the current meaning.