I hope you still enjoyed the game thought!
The random movement was added fairly quickly late into development as just extra topic related mechanics. All I did was have a 1 in 60 chance each frame that it will do a large increase in velocity in the players input direction. Repeat this for both the x and y axis and you get this random movement on average every second. I then fine tuned the ammount you move and chance that you will move so that it is just enough that it makes some difference to your game but not to much to be a 100% game of chance.