That is a very bold claim. A message queue can have many different requirements: Some message queues tolerate lost messages, others don't. Some require a notification mechanism (i.e. a push model instead of a polling model). Other require precise management of dead letters.
All this to say that, yes, you theoretically CAN use SQLite as a message queue. But atomic operations are usually WAY lower on the "must have" list for a message queue than other parameters.
The easiest way you could verify this is by looking at the guarantees provided by some of the most known MsgQueues.
SQLite supports atomic operations - the key requirement of a message queue.