-tor is the Latin agent suffix. Verb rept-a-re 'to creep (along)' > rept-a-tor 'one which creeps'.

There is another Latin root serp- 'to creep', Greek herp-, which we encounter in the present participle serp-ens, serp-ent- 'creeping', and herpetology, the study of reptiles.

I don't know whether there's any etymological connexion between rep- and serp- and creep. (I must look it up for my own edification.) There's no obvious sound-law connecting them.

I'd never heard of reptatorial. The construction of an adjective on an agent like that also occurs in pictor-ial 'of or pertaining to a painter' and my favourite grallatorial 'of or pertaining to a stiltwalker (sc. a wading bird)'.