I've given the question "+1" beacsue it led me to look up what exactly a bullet chart is. Like the questioner, I have now done a little research and am convinced that a bullet graph needs to show progress achieved towards a particular goal.
Moving on, let us consider the other possibilities.
Bar charts and line graphs (we seem to be using chart/graph as equivalents) should have a scale showing the variable and a scale showing the frequency. This chart has neither, so it's not one of them. Although it may be close to being a very badly drawn "stacked bar chart"...?
The key feature of a pie chart is that the area devoted to a particular attribute is proportional to the frequency of that attribute. Normally they are drawn as portions of a circle, but a pie could be rectangular, in which case a rectangular pie chart might be possible (although I have never seen one before).
This chart has the property that area seems to be proportional to frequency, so I would go for pie chart. It even has the percentages which some pie charts include.