What they are basically saying is that viruses can use the Bitcoin blockchain to communicate with their authors. So for example the virus author could put code into the blockchain and the infected computers would all get that code from the blockchain and run it.

This is a concern to kaspersky because normally the viruses would connect to a server, called a command and control server, to receive new instructions from the virus' author and send back stolen data etc. So all law enforcement would have to do is shut down the command and control server and they can cut the virus authors access to the infected computers. However, if the virus was using a blockchain, there would be no central point of failure and cutting the authors access would be non-trivial.

Other security researchers also had concerns about the website pastebin.com for similar reasons, that it could be used for botnet communication: http://blog.spywareguide.com/2009/06/pastebin-botnets.html

Most people are going to read this article and take it to mean that computers can be infected via the blockchain. This is not true. What they are talking about is using the blockchain as a way for hackers to send instructions to infected computers.