There is no requirement for a commercial airport to have an ILS. Obviously in parts of the world with regular bad weather then an ILS Cat I/II or III is necessary to keep things moving.
SXM has a non-precision instrument approach, a VOR/DME. Non-precision means an approach aid with no glide slope information, NDB(non directional beacon) and SRA(surveillance radar approach) are other types on non-precision approach aids. Lots of major airports in the US only have ILS’s on one or two runways but have non-precision aids on the others for when the weather is better i.e. 80% of time.