In addition to the regular county vote, the "Absent Railroad Vote" was 153 for Otero, 23 for Sargent, and 2 for Frost. The 1917 Blue Book lists these votes by county but that table only lists 1 vote for Frost, so clearly there is a disconnect there.
Source for Popular Vote data: New Mexico Secretary of State, "For State Auditor," Tabular Statement of the aggregate vote cast in the State of New Mexico (Santa Fe, 1916)