Read the PDF about making mead in the FAQ sticky. It did not mention anything about bottling. Does this mean I can simply transfer it to my bottles that I usually use for beer and let it age?
Yeah, many meads are still. Use the oxygen absorbing caps for longer storage...
If you want a still mead (no carbonation) than yes. If you want a sparkling mead (carbonated) than you need to add priming sugar.