That's not a protein shake, it's a weight gainer. It has protein and high quality carbohydrate in, both of which are needed to gain weight.
And yes, the extra calories will help you. Gaining weight is a matter of a simple energy equation: calories in > calories out. For some people the calories in will need to be 2500, for some they will need to be 3000, for some they will need to be as many as 5000.
At the moment you are not eating enough and you quite probably have a very fast metabolic rate, so the amount of calories you're eating is less than or equal to the amount of calories your body is burning. Obviously a weight gain drink will help you add those much needed calories into your diet, and combined with working out, you should start packing on some muscle. As long as you make sure you get enough carbohydrate, fat and protein from the rest of your diet you should find yourself gaining weight.
Although personally I don't see why weight gain drinks are necessary. I don't know anybody who needs to eat more than 5000 calories a day to gain weight, and if your metabolism is that fast then you don't have to worry about getting fat, just eat a couple of pizzas on top of the normal 3000 calories a day. Hell, if you're concerned about your health then boil up 250 grams of wholemeal pasta and cover it in fat free cheese and you've got well over 1000 calories right there. Oats and rice are also very calorie dense sources of quality carbohydrate, have yourself a really, really big bowl of ready brek or porridge with a load of sultanas and it will easily be as much as, or more than, 1000 calories.
In conclusion, the weight gain drink will help, but make sure the rest of your diet is in line first. Work out, and remember, above all, if you're not gaining weight, then quite simply you're not eating enough, so eat more carbohydrates and more protein (shoot for at least 180 grams of protein a day. At your weight, that should be enough).