The will to complete a task is a state of mind. Talking about a "finite supply of willpower" implicitly treats willpower as a substance, rather than a computational state. It's like claiming that a computer has a "finite capacity to run emacs," and you're using this precious capacity up by playing video games.
See Perceval's comment above that links to studies showing that glucose levels influence willpower. In other words, it is basically a physical substance on some level.
