Has an MLB game ever ended 16-10?
It has. 16-10 has been a MLB final 38 times in 235,971 games. The first was Chicago White Stockings beat Hartford Dark Blues on September 27, 1876; the latest was Cincinnati Reds beat Milwaukee Brewers on April 21, 2015.
That makes 16-10 the 151st most common final score out of 330 that have ever occurred in MLB. One point away, 17-10 has happened 20 times and 16-11 has happened 26 times. At one point the score disappeared for 28 years, between 1955 and 1983.