The link Traffic control signals says "Drivers facing a traffic control light with a green arrow and solid green traffic control light may enter the intersection and proceed without yielding in the direction indicated by the arrow. Drivers facing the green light may also proceed in the other directions when it is safe and legal." What does "other directions" it refer to in this case? Any direction other than straight and left? Thank you!
Yes, "other directions" refer to the layout of the roadway beyond the traffic signal appropriate for vehicles facing the aforementioned traffic control light. One could have a right turn lane immediately after the traffic control light and realistically, there could be a green arrow for that lane as well as a green arrow for left turns (more common).
When crossing traffic from the other direction is not a factor, the green arrows provide for movement of vehicles that might otherwise be required to be detained.
Your linked site references a flashing green signal, which I have not seen in the USA, probably because it is the equivalent of a non-flashing green signal.