Read the law first. (Score 1)

The text of the law (in Russian) is available here: http://www.pravo.by/pdf/2011-134/2011-134(010-029).pdf (first page, registration number 2/1869).

Google translation of subject matter bellow:

"Article 22.16. Violation of requirements for the use of the national segment
Internet
1. To work on the sale of goods, works and
services in the territory of the Republic of Belarus with the use of information networks,
and resources with an Internet connection is not located on the territory of the Republic of Belarus and (or) not registered in the prescribed manner -
punishable by a fine for an individual entrepreneur or legal entity
in size from ten to thirty basic values.
2. Violation of the requirements of legislation to implement the identification
subscriber units in the provision of Internet services and (or) users of Internet services
points of the collective use of the web services, recording and storing information about the subscriber's devices, personal data of users of Internet services, as well as information about Internet services rendered -
punishable by a fine of from five to fifteen basic values.
3. Breach of the law to restrict user access inernet services to the information gap for distribution in accordance with
legislation -
punishable by a fine for an individual entrepreneur or legal entity
in size from ten to thirty base units.. "

So, I don't see the problem for person in Belarus to log into amazon or gmail as long, as it is performed for personal, educational or other non-commertial purposes. Problems starts if you want to do business and your systems are outside of the country. And this most likely affects businesspeople from other countries visiting .by.

Of course, it is Belarus. And how widely this law will be [ab]used remains to be seen.