It's not genitive - technically speaking it's accusative of the possessive "jego", but in fact the pronouns "jego" - his, "jej" - her(s) and "ich" - their(s) do not decline so they keep the same form regardless of the case.
Also, even if the sentence were "Znam twojego psa" - the possessive pronoun "twojego" and all the others (except for the 3rd person possessives) have the same form in gen. singular and acc. singular :)
I hope it helped a bit :>
jego (here meaning "his") does not change according to case, gender, or number
Its an exception, unlike mój, moja, moje etc.
the word jego has another meaning as a PRONOUN, where it is part of a declension scheme
e.g. nie widzę jego (I don't see HIM)
but its not used as a pronoun here