What does negative pressure mean in the context of this manometer?
The manometer shown doesn't measure absolute pressure, just relative pressure. In this car the pressure of the gas in the closed tube versus the pressure of the gas in the bulb. 

As you have drawn it, the pressure of the fas in the tube is higher. If you measure pressure in the bulb relative to the pressure in the tube the answer is negative. If you measured absolute pressure (which this manometer can't do because of the lack of any external reference in the closed system) both would be positive but one would be higher than the other.