Context. Observational studies have widely demonstrated that galaxy physical properties are strongly affected by the surrounding environment. On one side, gas inflows provide galaxies with new fuel for star formation. On the other side, the high temperatures and densities of the medium are expected to induce quenching in the star formation. Observations of large structures, in particular filaments at the cluster outskirts (r > 2r₂₀₀), are currently limited to the low redshift Universe. Deep and wide photometric data, better if combined with spectroscopic redshifts, are required to explore several scenarios on galaxy evolution at intermediate redshift. Aims. We present a multi-band dataset for the cluster MACS J0416.1-2403 (z = 0.397), observed in the context of the Galaxy Assembly as a function of Mass and Environment with the VLT Survey Telescope (VST-GAME) survey. The project is aimed at gathering deep (r < 24.4) and wide (approx. 20x20 Mpc²) observations at optical (u, ɡ, r, i, VST) wavelengths for six massive galaxy clusters at 0.2 < z < 0.6, complemented with near-infrared data (Y, J, Ks, VISTA, ESO public survey GCAV). The aim is to investigate galaxy evolution in a wide range of stellar masses and environmental conditions. This work describes the photometric analysis of the cluster and the definition of a density field, which will be a key ingredient for further studies on galaxy properties in the cluster outskirts. Methods. We extracted sources paying particular attention to recovering the faintest ones and simultaneously flagging point sources and sources with photometry affected by artifacts in the images. We combined all the extractions in a multiband catalog that is used to derive photometric redshifts through spectral energy distribution (SED) fitting. We then defined cluster memberships up to 5r₂₀₀ from the cluster core and measure the density field, comparing galaxy properties in different environments. Results. We find that the ɡ – r colors show bimodal behaviors in all the environments, but the peak of the distribution of red galaxies shifts toward redder colors with increasing density, and the fraction of galaxies in the blue cloud increases with decreasing density. We also found three overdense regions in the cluster outskirts at r ~ 5r₂₀₀. Galaxies in these structures have mean densities and luminosities similar to those of the cluster core. The color of galaxies suggests the presence of evolved galaxy populations, an insight into preprocessing phenomena over these substructures. We release the multiband catalog, down to the completeness limit of r < 24.4 mag.