Paintball "guns", which are actually called paintball markers, do not use cartridges like firearms. They are basically air guns that use loose paint pellets.
If the entire reason Officer Vlasik entered the competition TV show was to investigate Akeny for his war crimes, she had to have known the entire time he was a dangerous war criminal and mass murderer. Under these circumstances, it makes no sense for her to stalk him in a deserted place, in the dark, armed only with a prop gun and with nobody to back her up.