This is a curious case which will need to be addressed by the nearest Costa Rican Consulate. Costa Rica provides a waiver of visa for people who have a visa with at least one day validity stamped in their passport. This is the same text that exists for the holders of the US Student (F, J) or work (H, G, etc) visas (sorry can't copy the exact text for some reason).
Now with that said the question becomes what exactly stamped means in this context since most visa "stamping" actually refers to something entirely different than an actual stamp.
You will not have one like this when you under under US Visa Waiver program. So whether or not the border control in Costa Rica will accept the arrival stamp as a valid US visa is still to be determined but I would suggest you don't take that chance and get a Visa from Costa Rica though I am not sure who is currently representing Costa Rican interests in Taiwan since the Embassy was closed in 2007. Unless you already have valid visas for other waiver destinations like Schengen or Japan.