You've already gotten some good advice regarding what you've written, so I'll focus more on what you've brought up here.
Structure
To have better structure, I'd say you can either plan more now, or revise things later.
Planning
People plan differently, and some plan more than others. There is no wrong way to do it, but it is worth experimenting to find what works for you. Some people prefer to just write as they go, with minimal (or no) planning.
I'd advise looking at your main idea, a talking dog with his owner and sister save the world from an evil alien, and thinking about some of the details you'll want to cover along this quest (your comic can serve as inspiration).
With a storygame, there will be choices, and those tend to be impactful. Will there be a path where they fail? What about a short path where they don't even try to save the world?
While thinking about this, be careful not to go overboard, since scope creep is a common problem. Think about the most important and most interesting paths, and focus on them.
When writing scenes and offering choices, try to have them be relevant to the story you're trying to tell, so that you might keep things moving forward! Always move forward towards some ending.
Also, be sure not to let planning get in the way of writing, since it is very much possible to just plan forever! Got to start writing at some stage.
Revising
You can always improve a story by making changes (removing or adding things) after having the first version written. In fact, your 3rd-grade comic is kind of the first version (but comics and storygames have some big differences).
You've already identified issues with your past work, so just improving those elements is a great goal. Just in case it proves helpful, one way to deal with characters who don't have a purpose is to combine them into one. This means there are less characters, but the characters that are there have more impact (since they affect more things).
Some people just want to share what they’ve written when they have the first version done. This isn't necessarily bad but proofreading shouldn't be skipped! Anyway, revising the work and making bigger changes is something that does get overlooked at times, which is why I wanted to mention it.
Conclusion
Think about where the story is going, and keep thinking about it as you write, that way you can make meaningful progress.
What should the next page be? You're thinking about it already, but if you haven't come up with anything, I'd say consider the alien!
I don't expect you to introduce them on the next page, but you could think about where/when you WILL introduce them, and start writing towards that moment (since it seems important for the story).
That's my advice, hopefully there's something there for you to consider.
Oh, and do keep writing! Consistency is powerful here.