How much is a "splash"
I would measure a splash by the second - that is, holding the container (usually bottle) about a foot above the pan, and pour about a second or two's worth of liquid.  Or to put it another way, stop pouring about when the stream of liquid hits the pan and consider that mid-air-stream a (medium) "splash".  

I would usually get a couple tablespoons of liquid pouring this way.  Of course, stronger liquids usually come in smaller mouthed bottles so less gets poured - for soy sauce, I'd get a few teaspoons, for water (from a cup) a few tablespoons, for something like liquid smoke - a few drops since the bottle's opening is very small.

More generally speaking, I've always considered "splash", "dash", "sprinkle" and other such measurements to be an equivalent for, like oft cited for salt and pepper, "to taste".  Or perhaps "to texture", depending on the what-where-when that's being added.  The recipe doesn't have a measurement because it isn't recipe-critical how much is actually added, it's just to the preference of whoever is cooking.