How is it possible for other animals to have better night vision than humans, who can detect individual photons?

That research shows that humans can detect single photons, not that we're particularly good at it.

Averaging across subjects’ responses and ratings from a total of 30,767 trials, 2,420 single-photon events passed post-selection and we found the averaged probability of correct response to be 0.516±0.010 (P=0.0545; Fig. 2a), suggesting that subjects could detect a single photon with a probability above chance. (emphasis mine)

This study showed that we could do better than random chance, but not that we could do substantially better than random chance.

Based on the efficiency of the signal arm and the visual system, we estimate that in ∼6% of all post-selected events an actual light-induced signal was generated (Methods section).

The quote you made from Wikipedia includes one of the major reasons for the superior night-vision in animals: Tapetum lucidum. The tapetum lucidum is a layer just behind the retina which is reflective; as the light enter the eye and hit the retina, it is not fully absorbed by the retina but instead passes through and hits the tapetum lucidum. The light is then reflected back, hitting the retina again which effectively makes the eye double the amount of available light. The light reflected by the tapetum lucidum is also the reason why many animals seems to have glowing eyes when you shine a light at them during low light conditions.

Humans, and other primates, lack the tapetum lucidum and, as we humans also have fewer rods than many other animals, the result is that we get a poorer night vision even though our eyes have the capability of detecting single photons.

And it's also pretty much a question of wavelength sensitivity. Being very good at spotting 532nm radiation is not very useful at night. Seeing IR is.