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TL, DV, and HAML contributed equally to this work. DV is grateful for support from the Studienstiftung des Deutschen Volkes. We acknowlege funding from the European Research Council under the European Union's Seventh Framework ERC Grant Agreeement No. 615613 and from the German Research Foundation (DFG) via Project No. Re2974/3-1 and the Research Unit FOR2414. ; We investigate the switching of the coherent emission mode of a bimodal microcavity device, occurring when the pump power is varied. We compare experimental data to theoretical results and identify the underlying mechanism based on the competition between the effective gain, on the one hand, and the intermode kinetics, on the other. When the pumping is ramped up, above a threshold, the mode with the largest effective gain starts to emit coherent light, corresponding to lasing. In contrast, in the limit of strong pumping, it is the intermode kinetics that determines which mode acquires a large occupation and shows coherent emission. We point out that this latter mechanism is akin to the equilibrium Bose-Einstein condensation of massive bosons. Thus, the mode switching in our microcavity device can be viewed as a minimal instance of Bose-Einstein condensation of photons. Moreover, we show that the switching from one cavity mode to the other always occurs via an intermediate phase where both modes are emitting coherent light and that it is associated with both superthermal intensity fluctuations and strong anticorrelations between both modes. ; Publisher PDF ; Peer reviewed