Why is Specific heat of Ammonia higher than water?
The link in the question states that ammonia has a higher specific heat than water. This is true, but it is important to compare the specific heat values under identical (or very similar) conditions.

The isobaric specific heat of ammonia (gas) is 2.1636 kJ/kgK at 1 atmosphere and temperature = 26.9 C. https://www.engineeringtoolbox.com/ammonia-heat-capacity-specific-temperature-pressure-Cp-Cv-d_2016.html At -33.6 C (boiling point of $NH_3$ at 1 atm), the specific heat of $NH_3$ gas is 2.2946 kJ/kgK, not much different from the gas at 26.9 C; however, for liquid $NH_3$ at 1 atm and -33.6 C, the specific heat is 4.4464 kJ/kgK, a large increase from the gas at that temperature.

Liquid water has one of the highest specific heats among common substances, about 4182 J/(K kg) at 20 °C https://en.wikipedia.org/wiki/Specific_heat_capacity At 100 C, liquid water has a specific heat of 4.2157 kJ/kgK (implied pressure = 1 atm). Again, not much difference because of temperature. https://www.engineeringtoolbox.com/specific-heat-capacity-water-d_660.html Now we find water vapor data in a different place: https://www.engineeringtoolbox.com/water-vapor-d_979.html where gaseous $H_2O$ at 216 F (102.2 C) has a specific heat of 1.890 kJ/kgK, a large drop, even bigger than in the ammonia system.


So although it is often stated that water has one of the highest specific heats among common substances, it seems that either ammonia is not considered common for this issue, or yes, it's true that water has one of the highest specific heats...And that is true of the gas and the liquid states!
But then among all the data, which are truly interesting, there is one other thing that stands out: the heat of vaporization of water is 40.8 kJ/mol, whereas for ammonia, it is only 23.5 kJ/mol. So water can still be considered an extreme molecule.