Can an infrared thermometer (IR gun) be used to measure the ambient room temperature?
In the relevant part of the infrared spectrum for this application\$^1\$, air has a high transmittance:



(taken from here licensed under  Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License)

So wherever you point an IR temperature sensor, the output will be dominated by the surface you are pointing at and not the air in between.

If you try and point an IR sensor in the sky (no clouds) you will get a a very low reading (mine showed −40 °C but that is the lower range end), and not the air temperature.

So you need some surface at room temperature to measure the room temperature. Do not use shiny metals, as those reflect IR radiation. Normal glass can be used, so you could hang a decorative looking thing in the room and measure the surface of that – provided you have a small enough measuring cone (so it only hits your wanted surface and not something behind it).



\$^1\$: For −40 °C the peak in IR is around 15 µm, for 50 °C the peak is around 8 µm.



The sensor you linked uses a thermopile (a stack of thermocouples). These sensors require knowledge of the ambient temperature to calculate the targets temperature. So integrated into the IR sensor is an ambient temperature sensor, and the measured value can actually be read out, so you get the ambient temperature of your sensing element. Depending on the location where you place it, that might be close enough to room temperature already. But in that case the IR part looses its use and you could just use a normal temperature probe.