"Might not get + verb"

The idea of this phrase is that if you are 'driven', that is, you have a goal or dream and are actively working to achieve it, you will be less likely to 'get run over' (that is, beaten or out-competed) by, for example, others who are also 'driven'. Let's start by thinking about it literally: if you're a pedestrian who is trying to walk along a street where cars are traveling at high speeds, it is very likely that you will 'get run over'; that is, a car will hit you. You will also be able to travel much less distance in the same amount of time as a car. But if you are instead driving a car on that same street, you can travel at the same high speeds that the other cars are traveling, and therefore you are less likely to 'get run over'.

Now if we think about it figuratively, the pedestrian is someone who is not 'driven' (motivated/pursuing goals), and is instead passive and not going anywhere relative to other people around him who are 'driven'. Because the pedestrian is not moving where everyone else is moving, he is more likely to 'get run over' because he gets in the way of everyone else. The claim of the phrase is that if you are motivated and pursuing your goals, you will have some 'direction' and 'momentum' that makes it less likely that other people who are also pursuing their goals will intentionally or unintentionally damage you in the pursuit of their goals. The pun is trying to make a connection between both the literal and figurative meanings of 'drive' and 'run over' to make a point about competition between people.