No one governs the board of a nonprofit, exactly. In this case, it sounds like Sam and his allies are trying to exert pressure on the board by threatening crippling resignations. This puts the board in the position of choosing between pursuing its mission without certain employees, or pursuing business plans that do not align as well with its mission, but with the full complement of employees.
It's a tricky situation (and this is just with a basic/possibly-incorrect understanding of what is going on). I'm sure it's much more complicated in reality.