The answer is, it depends. In the case of they are not classified as an MSB, because they do not have access to your funds.

In their legal description they claim:

5.1.1 The Wallet is provided to you exclusively by Blockchain Luxembourg S.A. At no point will Blockchain ever take custody or control over Virtual Currency stored in your Wallet. The Wallet is only capable of supporting certain Virtual Currencies. Under no circumstances should you attempt to store Virtual Currencies in your Wallet that the Wallet does not support. The Wallet does not store, send, or receive Virtual Currency.


So, in view of the above. They would not be a money transmitter. If other wallet providers also, behave the same way, then no money transmitter license is required.