This is actually a historic curiosity. Not just does the DR have an unusual disproportionate amount of good baseball players, they also all have several traits in common that are a give-away of the reason: they are mostly from the San Pedro de Macoris area of the island, have often non-Hispanic last names and are of a darker skin-color than the average Dominican.
In other words, it's in the DNA.
Robinson Canó, born in San Pedro de Macoris
From 1800 to 1920 the DR saw a massive influx of non-Hispanic Afro-Caribbean immigrants from other Caribbean islands that were invited to work on the sugarcane plantations. They brought with them their culture that had strong British roots: music, the English language, their Anglican religion, English last names -- and cricket. They became known colloquially as ‘cocolos’.
While baseball was known and played already thanks to the American occupation and Cuban refugees, especially the eastern part of the island around San Pedro de Macoris enjoyed a mostly-cricket fandom due to the large Cocolo population. Cricket clubs and teams had sprung up all over the place and all was set for it to become the most popular sport on the island.
Dominican Republic’s provinces where people of Cocolo ancestry predominate
However, in 1916 the US occupied the island to protect their interests, and took over the government, the military, the police and especially customs and immigration. The influx of immigrants was stopped for anyone not Caucasians, and the occupation forces began to ‘Americanize’ much in the country. Cricket too fell victim to this.
By the 1920s the plantation owners -- mostly Americans -- were willing to pay cricket-players to play baseball and were willing to support baseball teams and not cricket teams.
Cricket thus died out. Talented cricket players turned to baseball since there was no money to be made in cricket. Dominican dictator Trujillo also encouraged local baseball and from the 1950s onwards the game flourished on the island. Eventually US Major League Teams began setting up their own training camps and scouts traveled the island to find more players, but the majority are those of Cocolo, cricket-playing blood.