Right now, the point of the exercise is to have Russian internet infrastructure continue to function if all the international internet links get severed. There are technical challenges in that (for example, DNS system, which translates website names to actual internet addresses, others involve traffic routing, which generally don't respect country borders). As for other services, those that don't have (self-sufficient) servers inside Russia would vanish.
2nd order effect of this exercise is to identify and control all the 'ingress points' of the network into Russia. This would produce the capability to effectively control (and censor) all the data coming in and out of the country. There's high likelihood that this is in fact the real reason to do this.
Now, if this capability to sever all links was ever actually employed, yes, it would be impossible to send an email from Russia to Germany, for example. Obviously, this would be a severe disruption and huge problem for both companies and citizens. But, let's have some perspective: Russia is among the countries that stockpile weapons which are capable of killing billions in minutes. Being able to cut off internet is not a huge outlier here. :-)