Regarding the definitions of the words, (jig, reel, hornpipe etc.) it's my belief that they were first coined to describe the dance, hence the way the dictionary treats them. To call a jig (music) a jig is by no means wrong, but knowing why leads to a greater understanding of the music even if you never play it to be danced to.

The dances themselves could be danced to no more than percussion instruments if necessary, just as the tunes can justifiably be played without dancers. I'd guess that the very first dancing humans ever did was to no more than thythmic percussion, not melody.