Missing grounding rod is a safety issue / an electrical code requirement; water pipe cannot be the only grounding electrode. However, depending on a jurisdiction and adopted / enforced code in your area, you may not be required to perform such improvement, even if it is a safety concern.
Some jurisdictions go after safety issues and attempt to enforce them even if there were no major electrical updates performed in a property. Others may request to install the second grounding electrode only when updating electrical service.
It would definitely be safer to have that grounding rod installed, it shouldn't be that expensive.