If you read the article more closely, you will notice that Podemos is demonstrating to change the arrangements that Spain is a party to, not to leave them. They are not looking to take Spain out of the Euro. They want to reform the Euro. This is also clear in the Podemos manifesto (see the link in my earlier post).
If this had been a demonstration calling for Spain to leave the Euro, then you might have a viable case for investing in gold, on the reasonable grounds that a break up of the Euro would collapse the European banking system, and the US banking system as well. But is isn't.
Afterthought: There is a demonstration in Sol (the major square in Madrid) on most weekends. This is one of the bigger ones. (One of the things I like about the Spanish is the way they value their democratic rights and a prepared to get out in the streets to exercise them. This is something that most Australians don't really get - never having lived under a military dictatorship.)