Here we have another idiosyncratic error in the 1841 British edition, the replacement of this with his. This typo, a visual error, was corrected in the subsequent LDS edition (1849). Clearly, this works better. For other examples where the 1841 typesetter mixed up this and his, see under Helaman 8:22.
Summary: Retain the determiner this in Mosiah 1:10: “thou art a king and a ruler over this people”.