Context.A majority of massive stars are part of binary systems, a large fraction of which will inevitably interact during their lives. Binary-interaction products (BiPs), that is, stars affected by such interaction, are expected to be commonly present in stellar populations. BiPs are thus a crucial ingredient in the understanding of stellar evolution.Aims.We aim to identify and characterize a statistically significant sample of BiPs by studying clusters of 10 − 40 Myr, an age at which binary population models predict the abundance of BiPs to be highest. One example of such a cluster is NGC 330 in the Small Magellanic Cloud.Methods.Using MUSE WFM-AO observations of NGC 330, we resolved the dense cluster core for the first time and were able to extract spectra of its entire massive star population. We developed an automated spectral classification scheme based on the equivalent widths of spectral lines in the red part of the spectrum.Results.We characterize the massive star content of the core of NGC 330, which contains more than 200 B stars, 2 O stars, 6 A-type supergiants, and 11 red supergiants. We find a lower limit on the Be star fraction of 32 ± 3% in the whole sample. It increases to at least 46 ± 10% when we only consider stars brighter thanV = 17 mag. We estimate an age of the cluster core between 35 and 40 Myr and a total cluster mass of 88₋₁₈⁺¹⁷× 10³M_⊙.Conclusions.We find that the population in the cluster core is different than the population in the outskirts: while the stellar content in the core appears to be older than the stars in the outskirts, the Be star fraction and the observed binary fraction are significantly higher. Furthermore, we detect several BiP candidates that will be subject of future studies.