It appears that I have to create a game as a separate project. If this is true, can that game be expoted to a slide in a previoulsy made project?
You can create a game in an existing project or as a separate one. It depends on your needs.
If you create a game as a separate project, you can export it to HTML5.
See this tutorial for details: How to Export Projects to HTML5 in ActivePresenter 8
After that, insert the exported HTML5 package into a slide in your previous made project as described in this tutorial: How to Add Web Objects in ActivePresenter 8 - Atomi Systems, Inc.
How do I create it in an existing project. I tried, but it creatd an entire new project?
You can add new slides to the existing project (Home/Insert tab > New Slide).
Then, design game as you did in a new project.