HTML + Blender game engine? The diagram is of a river bank with a formula that can be adjusted with sliders to calculate the river's area, steepness, vegetation population, etc.

The question is, is it possible to do this in blender somehow, either with the game engine or drivers, so that sliders could change not only numerals but also the look of the river diagram?

I have pretty much zero experience with the game engine (but years with anything else to do with Blender) and before trying anything out I wanted to know if it was possible to do something like this.

I have also seen this recent link to the game engine working on browsers and was wondering if this could work for this too?

http://www.blendernation.com/2014/07/11/blend4web-an-interactive-3d-viewer/
According to the documentation Blend4web uses WebGL and supports:
Full Support

Yandex Browser
Chrome
Firefox
Opera

Experimental Support

Internet Explorer 11
Safari 8

Mobile Platforms

Android (on the majority of modern devices)
BlackBerry
Firefox OS
iOS 8
Tizen
Ubuntu Touch
WebOS

It looks promising, I would check whether it covers all requirements and give it a try.