After reading what Dmitry Khomitchuk said (who after all has a personal interest in this),
I am saying that the impact of the law is probably exaggerated. There is a propaganda war against Belarus so it's natural that something like this is used.
Lots of countries have
more internet monitoring and censorship than Belarus.
Australia, South Korea, France, Thailand and China to mention places where you might find yourself on holiday or business. You have more reason to worry there, than in Belarus.
In the USA you should start worrying about SOPA for example (own goal by Pavelov to link to an article about that, lol!)
This map is from Wikipedia's entry on internet censorship
Wikipedia quotes
But let's get to the bottom of this.
I have read the articles now, and just to re-assure myself, I'd like to ask anyone who is in Belarus to try three things: 1) Go to the most anti-government / anti-Lukashenko website you know of (in Russian) and make sure it is not blocked for you.
2) Go to a site that does not have a .by extension and check if you are able to buy something online. (I mean, don't actually buy anything, just check if it is possible to take the purchase up to the point of sale without actually buying.
3) Have you got unrestricted access to the site Vkontakte.ru?
If both these things are possible, then we have proved that the law is nothing to worry about.
And make no mistake - I hate internet monitoring and am all for a completely free internet. But it does not seem to me that the situation in Belarus sticks out as a big problem.