The answer is
I run off of a cup of joe
Minecraft is written in Java (a language and also another name for coffee)
I virtualized the sandbox
You play in a virtual sandbox world.
And brought construction to the poor
The game lets anyone create/construct things in a virtual world.
Some exploited me, and rose to wealth
You can apparently make money selling Minecraft perks and services. (source)
My founder once was loyal, But now he left, a billionare
Markus Persson founded Mojang, the company that created Minecraft. He stayed for 4 years before selling out to Microsoft for $2.5 billion.
The company that bought me-, Both small and big-, With a worldwide influence
Microsoft is a huge company with worldwide influence. "Micro" means small.