My client is purchasing a property by means of seller financing. I know that lenders require a mortgagee, or lender, title insurance policy to protect the lender from any problems with the title, but would the buyer in this case still have to provide a mortgagee policy to the seller?

Yes, if you're using the TREC contracts. Paragraph 4C of the TREC contracts state that if an owner policy of title insurance is furnished to the buyer in a seller-financing transaction, then the buyer has to provide the seller with a mortgagee policy of title insurance.