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I don't really know about the silence gap, so I just extracted a bunch of .wav from RS4_audio.bnk and loaded all of them in imhex (an hexadecimal editor) and upon opening it told me that the "RIFF/WAVE/PCM (.wav)" pattern was compatible, and I applied it, basically meaning it recognized the file looks like a .wav file and told me there's a thing I can load to tell me what all those values in the files mean.
Anyways using that I can tell you all the file had:
"WaveFormatType" of "MS_ADPCM" 1 Channel 44100 samples per second block aligned at 1024 4 bits per sample extended data size of 32 2036 samples per block Now 1 Channel, 44.1K samples and 4 bits per sample I understand, but "MS_ADPCM" seems to be refering to how sample data is stored as another possible value for "WaveFormatType" is "IEEEFloatingPoint" (I suppose depending on the value of that field amplitude could be stored either as integer or floating point values) and as for the rest of that idk what it means but I don't think it's important and I don't know how to export in that exact format anyways.
I reckon either the silence gap is due to user (or software) error or due to file format and that is the exact format the game use so hopefully this helps you export it correctly, probably dig around in audacity's setting or the internet.

As for the click at the end of the audio, that's because you want the amplitude of the first and last sample in your loop to be at 0 or at least the same value, so cut it such that it ends and begin at a "zero crossing".
The reason being that if you loop start with an amplitude value of +1 (meaning the speaker membrane is all the way out) assuming no sound is playing (so the current speaker membrane position is at 0) when you start to play the sample the membrane will suddenly (in 1/44100 of a second) jump from the resting position (0) to all the way out (+1) pushing out a bunch of air that you will hear as a "click", if the sample ends at an amplitude of -1 (membrane all the way in) the same thing will happen when it loops back but even worse since the amplitude change is now double (ends at -1 -> +1 in 1/44.1K of a second).
Also for what it's worth listen to it in-game because when I looped one of the RS4 sounds in vlc it clicked, yet I never heard a click in-game (maybe because the loop begins and end at the same amplitude but in vlc there was a tiny delay before it looped allowing the speaker membrane to go back to rest (amplitude 0) and then it jumped back when it started again).
 
Anyways, sorry for the wall of text hope this helps