Watchout only uses Quicktime when exporting a movie, so it would make little sense to install Quicktime on a display computer. If you want to use the export function in Watchout, Quicktime is required on the production computer.
That said, if you want to encode to Hap using a Quicktime-enabled application, you might need to install Quicktime and the Hap codec for Quicktime. Another option would be to encode Hap files using ffmpeg, using the following command line:
ffmpeg -i inputfile.mov -vcodec hap -format hap_q -chunks 4 outputfile.mov
Change hap_q to hap or hap_alpha if you want standard hap or hap with alpha. The chunks argument enables multithreaded decoding, but higher numbers give slightly more overhead, both in space and decoding time, so this number should be kept as low as possible. For a 1920x1080 video, one chunk is sufficient on most hardware. Higher resolutions and/or slower hardware might require a larger number. It never makes sense to use a larger number than the number of cores in the CPU.