We present comprehensive observations and analysis of the energetic H-stripped SN 2016coi (a.k.a. ASASSN-16fp), spanning the {gamma}-ray through optical and radio wavelengths, acquired within the first hours to ~420 days post explosion. Our observational campaign confirms the identification of He in the supernova (SN) ejecta, which we interpret to be caused by a larger mixing of Ni into the outer ejecta layers. By modeling the broad bolometric light curve, we derive a large ejecta-mass-to-kinetic-energy ratio (M_ej_~4-7M_{sun}_, E_k_~(7-8)x10^51^erg). The small [CaII]{lambda}{lambda}7291,7324 to [OI]{lambda}{lambda}6300,6364 ratio (~0.2) observed in our late-time optical spectra is suggestive of a large progenitor core mass at the time of collapse. We find that SN 2016coi is a luminous source of X-rays (L_X_>10^39^erg/s in the first ~100 days post explosion) and radio emission (L_8.5GHz_~7x10^27^erg/s/Hz at peak). These values are in line with those of relativistic SNe (2009bb, 2012ap). However, for SN 2016coi, we infer substantial pre-explosion progenitor mass loss with a rate dM/dt~(1-2)x10^-4^M_{sun}_/yr and a sub-relativistic shock velocity v_sh_~0.15c, which is in stark contrast with relativistic SNe and similar to normal SNe. Finally, we find no evidence for a SN- associated shock breakout {gamma}-ray pulse with energy E_{gamma}_>2x10^46^erg. While we cannot exclude the presence of a companion in a binary system, taken together, our findings are consistent with a massive single-star progenitor that experienced large mass loss in the years leading up to core collapse, but was unable to achieve complete stripping of its outer layers before explosion.