It may or may not affect the Steem blockchain.
First and foremost it is important to make the required distinction between Steem, the blockchain, and Steemit.com, the app/interface operated by Steemit Inc.
Considering that Steemit Inc. is based in the USA, the new EU directive will not have any impact on Steemit because Steemit falls outside of the EU legislative since there is no EU office.
When it comes to the Steem blockchain things may become slightly more fickle. First and foremost there has AFAIK not yet been any regulation about decentralized (content storage) ledgers like the Steem blockchain.
The new legislation could become a problem though, when takes effect, because many witness servers are hosted in Germany. Most likely to happen is that witnesses will relocate to countries where the laws do not require the measures enforced by the new directive, especially Article 13.
Note: IANAL, or as they say “I’m not a lawyer”.