Phosphorylates deoxyguanosine in the mitochondrial matrix with high efficiency but shows very low activity against other deoxynucleosides. 2'-deoxyguanosine + ATP = ADP + dGMP + H(+) kcat is 0.11 sec(-1) with deoxyguanosine as substrate. kcat is 0.30 sec(-1) with deoxyadenosine as substrate. kcat is 0.51 sec(-1) with deoxycytidine as substrate. kcat is 0.02 sec(-1) with deoxyuridine as substrate. kcat is 0.07 sec(-1) with deoxythymidine as substrate. Homodimer. Belongs to the DCK/DGK family.