'amphitheatre-like' is a compound formed from the noun 'amphitheatre' and the adjectival suffix '-like' (from Old English 'lic'), where 'amphitheatre' comes via Latin 'amphitheatrum' and Greek 'amphitheatron' and '-like' meant 'having the form of'.

'amphitheatre' comes from Greek 'amphitheatron' -> Latin 'amphitheatrum' -> Old/Middle English 'amphitheatre'; the suffix '-like' derives from Old English 'lic' (Middle English '-like') and became the productive English suffix meaning 'similar to', producing compounds such as 'amphitheatre-like'.

Initially 'amphitheatre' referred specifically to an ancient open circular or oval performance venue; combined with '-like' the compound came to mean 'similar in form or character to an amphitheatre' rather than the institution itself.