Intramolecular bonds are quite a bit smaller than intermolecular distances, so if you pack atoms into longer molecules you get a denser result.

I'm guessing very long molecules become problematic (because they don't pack well), but ammonia is a small molecule so way below that.

Liquid ammonia has a density of ~690 kg/m3 and a molar mass of 17 g/mol so ~40k mol / m3, as NH3 that's ~120k atoms of hydrogen per cubic meter. Meanwhile liquid hydrogen has a density of 71g/L and a molar mass of 2.02 g/mol so a very similar ~35k mol/m3 but as H2 that's only ~70k atoms of hydrogen per cubic meter.

And liquid hydrogen aside from being extremely flammable, can't exist above 30K and degrades storage material (https://en.wikipedia.org/wiki/Hydrogen_embrittlement), ammonia is much more forgiving and liquid at ambient temperature above 1MPa (10 times atmospheric pressure), not innocuous by any means but way easier to transport and store (storage requirements are similar to propane).