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 ) , i.e . 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 resolve the dense cluster core for the first time and are able to extract spectra of its entire massive star population . We develop 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 , two O stars , 6 A-type supergiants and 11 red supergiants . We find a lower limit on the Be star fraction of 32 \pm 3 \% in the whole sample . It increases to at least 46 \pm 10 \% when only considering stars brighter than V = 17 \mathrm { mag } . We estimate an age of the cluster core between 35 and 40 Myr and a total cluster mass of 88 ^ { +17 } _ { -18 } \times 10 ^ { 3 } M _ { \odot } . 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 .