The problem is, that legislation does not actually protect citizen data. All code is still controlled by LinkedIn, and Russian goverment still have no idea what it does. If FBI (or CIA or any other agency) comes to LinkedIn with an order, then does it matter if the technician serving the request pulls the data from Russian, European or US database? The data will be delivered anyway.
Moreover, the law does not actually prevent the companies from storing data somewhere else -- Article 12 mentions many allowed reasons to send the data to other countries.
What this law, however, allows is for government to apply pressure on the company by treating to seize their servers (such as this case: https://torrentfreak.com/police-shut-down-russian-rapidshare... ). I see no other reason for the law.