Technically, the term "Latin" or "Latino" is incorrect. If we take the meaning as it is, it correctly refers to someone who speaks Latin, the language that originated in Rome. Thus, if we say "is he Latin," we're basically asking "is he Italian?" Italian and Latin share many lingual similarities, but you're not asking if someone is of Italian origin. Correctly, you're referring to "Hispanics," which is the mix of cultures that constitutes a group of people of various origins. Hispanics, often incorrectly labeled as "Latinos," are not a race. Again, it is a group of people comprised of indigenous peoples, Spanish Penunsulares, Creoles, Zambos (not the Sambo of Confederate American caricatures), etc.
So the question should be if he is Hispanic, not Latin. Which in this case, he is because he is of Costa Rican origin.
Now if you're referring to his status as a Latin American (note the difference, Latin American, not Latin), the answer would also be yes, too. Latin is the building block of all Romance languages. This includes Spanish, French, Italian, Portuguese, Catalan, Romanian, etc. All countries in Latin America, with the exception of Belize, Guyana and Suriname, designate a Romance language as its official language.
Thus, the man you met is Hispanic. He is Costa Rican, yes, which means he is Latin American, not Latin.