Coincidence detection of single photons is crucial in numerous quantum technologies and usually requires multiple time-resolved single-photon detectors. However, the electronic readout becomes a major challenge when the measurement basis scales to large numbers of spatial modes. Here, we address this problem by introducing a two-terminal coincidence detector that enables scalable readout of an array of detector segments based on superconducting nanowire microstrip transmission line. Exploiting timing logic, we demonstrate a sixteen-element detector that resolves all 136 possible single-photon and two-photon coincidence events. We further explore the pulse shapes of the detector output and resolve up to four-photon events in a four-element device, giving the detector photon-number-resolving capability. This new detector architecture and operating scheme will be particularly useful for multi-photon coincidence detection in large-scale photonic integrated circuits.