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.
Anyone that is into Bitcoin should have decent, solid knowledge of how to keep a computer clean. If you are infected you are already screwed up.
I still don't get how the blockchain is going to be able to execute "code". All the blockchain does is verify hashes, given you aren't using some weird non common wallet.