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They used a different serif typeface and then modified the image. You won't be able to find the typeface with cracks (or ripples, as I see it), because it never existed. As for the typeface without cracks, I can't identify it. They might have used several, judging by how the descender on the "y" isn't curved like the "r" is.
Also, they probably didn't use a free typeface or one that comes packaged with your operating system. Professionally-made typefaces cost way more money than you think they do, so don't count on it being free or affordable.
Buuut maybe someone else can identify it?
But the title says "Cave Story" not "Cave Story+", so it indeed can be misleading. Also the post by X-Calibar already answers the question for CS+. I don't think it hurts to know the answer for the original as well.