I appreciate your thoughtful consideration! The concept of "insisting" does imply an intense desire or urging, which could bring in some elements of the subjunctive mood. In some cases, the phrase “that I throw” can suggest a recommendation or demand because it can imply that throwing the ball is what the dog desires or requires.
However, the majority of the sentence is presenting an observation about the dog's behavior in the present moment, which is why it leans more towards the indicative mood.
Your perspective highlights the subtleties in language, and it's great to engage in this kind of discussion! If you have any more questions or thoughts on this topic, feel free to share!