That seems like a pretty solid idea as it would really show the flexibility of the engine in one game. As far as ideas that would be great showcases for the engine, while pushing it to test, there are few that could be better than one incorporating major elements from several genres. With the right structure, it would be relatively easy to demo most game possibilities and engine features.
On the note of the "3 or 4 smaller games within the one", what could be done is elements of each "sub-game" could be present in one larger section (FPS, RTS, RPG, vehicle-use, etc), but have the smaller, "sub-game" focus more directly on each, woven into a seamless structure and story.
Say it opens up similarly to how NightHawk describes, but coming at the front of a large building that you're basically sieging. You have troops you manage, like an RTS, but eventually jump into the action, able to switch between combat and management (rather than a camera move to top-down, how about you manage from a third-person view with what you see instead of "globally"?), to make a push into the building. Once in, the game becomes mostly a squad-based FPS, where you can direct a squad. This is where other RPG elements could be shown as well, where you can up skills for both you and your squad members, and you fight through and take over the place.
It would obviously be shorter than a standard game, but as a demo, it could work really well. Any section could be as long or short as needed to really show stuff and it could really be any setting. Fantasy, sci-fi, modern, and would still work. Any number of other features could be added to the mix to showcase more, like a stealth element could be added to the FPS section, or even some form of racing at the beginning where you scout ahead before the siege, a patrol spots you, you chase them down in your vehicle to stop them, which could even lead to a branching event system where if you aren't able to catch him in time, the siege is more difficult.
I think really my main point is that there is a wealth of possibilities going off of the present idea.