Here, "chug" imitates the sound an engine makes while it is starting. chug chug chug Chug CHUG VROOOOOOOOOOOOOOOOM. "On a cold winter morning, Bob tried to start his car. It chugged for a long time, and then started to run smoothly." "chug into effect" is not a standard phrase. The printing press chugged while it came into effect, and since "chug" sounds similar to "come", the writer replaced "come" with "chug"

It's the noise that a printing press makes. We generally talk about a steam train chugging - i.e. it makes a chug chug chug sound as it gets going.

Chug could mean that it is working quickly, but could also mean that the machine reluctantly started. (Like an old car when you start it)

It means that the printing press is operating - the word "chugs" implies a machine that it is running but is often rumbling, cranking, grinding during operation.