How would this story flow differently if I had just written “So I ran to Hagrid's hut” instead of including this page?

For one thing, it would have been quicker and easier for me to write. That's one of my motivations, obviously. In fact, I want to get this story done as quickly as is possible without sacrificing quality, so if drawing something and just summarizing it are equally effective in the narrative, I'll go with the summary. If I draw something, it means that either it was quicker to draw it than to explain it (which sometimes happens), or it had an important effect that I couldn't achieve with a summary.

I can't actually be certain why I chose drawing instead of summary here. There are a few specific reasons I can think of, but I really made the decision based on instinct rather than logic.

Anyway, the first reason is that it establishes the setting – this way, you get a view of the outside of Hagrid's hut, and so you have more of a sense of where the action is than if you just saw the image of Harry inside the hut to begin with.

The second reason is that it dramatizes what's about to happen. What made Harry feel strongly enough that ze ran all the way to Hagrid's hut at a stretch? And what's going to happen when ze gets there? These are questions that you wouldn't have time to ponder if I skipped over the action of this page. (And we're going to be in Hagrid's hut for about three pages after this, so the hype is worth it – I wouldn't write a page-long setup to an event that was over in one page, unless it was REALLY important. But writing setup pages for sections that are larger or more important helps establish a structure for the story.)