Context. GRB 111209A, one of the longest gamma-ray bursts (GRBs) ever observed, is linked to SN 2011kl, which is the most luminous GRB supernova (SN) detected so far. Several lines of evidence indicate that this GRB-SN is powered by a magnetar central engine. Aims. We place SN 2011kl into the context of large samples of SNe, addressing in more detail the question of whether this GRB-SN could be radioactively powered, and whether it represents an extreme version of a GRB-SN or an underluminous superluminous SN (SLSN). Methods. We modelled SN 2011kl using SN 1998bw as a template and derived a bolometric light curve including near-infrared data. We compared the properties of SN 2011kl to literature results on stripped-envelope and SLSNe. Results. A comparison in the k, s context, i.e. comparing SN 2011kl to SN 1998bw templates in terms of luminosity and light-curve stretch, clearly shows SN 2011kl is the most luminous GRB-SN to date and is spectrally very dissimilar to other events because it is significantly bluer/hotter. Although SN 2011kl does not reach the classical luminosity threshold of SLSNe and evolves faster than any of these objects, it resembles SLSNe more than the classical GRB-associated broad-lined Type Ic SNe in several aspects. Conclusions. GRB 111209A was a very energetic event, both at early (prompt emission) and at very late (SN) times. We show in a companion publication that with the exception of the extreme duration, the GRB and afterglow parameters are in agreement with the known distributions for these parameters. SN 2011kl, on the other hand, is exceptional both in luminosity and spectral characteristics, indicating that GRB 111209A was likely not powered by a standard-model collapsar central engine, further supporting our earlier conclusions. Instead, it reveals the possibility of a direct link between GRBs and SLSNe.