grammar - Is 行く stative, continous or instantaneous?

My textbook says 行く is instantaneous (expresses changes from one state to another) and can only be used to describe the result of a change, not movements that are currently in progress. But a Japanese native has told me that it can be used to express an on-going action. For example

今父はコンビニにタバコを買いに行っています。

describes the father somewhere in the process of the action.

So, as you can imagine, I'm very confused with all this. Could somebody please clarify it a bit? Is my textbook wrong?