That is powdery mildew. Try to avoid getting the leaves wet in the future since wet conditions speed the growth and spread of the mildew. For me powdery mildew doesn't do too much damage and normally doesn't hit the plant until the vines are very large with fruit already on them. Your vine seems like it isn't too big, at least from the pictures you posted. Typically, as you have noted, powdery mildew kills the old leaves but the growing tip remains fine as long as it is vigorous. They do sell fungicides to control the mildew, but since the vine was wild anyway you might just want to hope for the best.