Of what "type" is this Mexican-Romantic music track?
The track is "Manny and Meche" from the 1998 video game Grim Fandango.
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This is a beautiful example of the Argentine tango, a type of music invented for the Argentine version of the famously intimate dance of the same name. To be exact, it is an example of "nuevo tango" style created by the Argentine composer Astor Piazzolla's influential fusion of the distinctive 3+3+2/8 tresillo tango rhythm with elements of jazz and classical music. Compare the following:
You might get closest to your example with some combination of these terms: "slow acoustic guitar argentine tango ballad." There are some particularly nice variations on this style by the Buena Vista Social Club.