While the engine I used Twine/Twinery 2 doesn't allow images & backgrounds itself, the files it publishes are pure HTML/CSS so if you know some tricks with these languages you can add them. It also supposed to support Javascript meaning you can do anything with it though I haven't tried Javascript myself yet.

The title image is one I added using < img > tag. the image don't appear through "debug" view in the engine, due to the way I added it. This didn't bother me, but if the game you're making depends greatly on images, I think you better off with another engine. Like Ren'py. Not that it's not possible with Twine, just not without coding.