Would not expect it to be an event in the Olympics anytime soon.
Target shooting and something like archery are considered sports. Both are in Olympics. Hunting with gun and arrow are considered a sport at least because they are covered on ESPN. Dodgeball is sport in where teams target other humans.
Therefore, Paintball which includes elements of all is a sport
Many people I meet claim that paintball is not a sport. However, it is possibly the most sport like activity ever. Paintball requires strategy, skill, athletic ability, teamwork and much more. Chess is considered a sport and yet it requires no physical exertion, only strategy. To all those who think paintball is not a sport, you have been proven wrong!
Many sport activities test one's physical endurance to an extent. Paintball certainly requires skills and endurance we all need to survive, where many other sports fall short in relevance. Paintball combines physical endurance, strategy, and skill. It can be a team effort or individuals competing as is the case with many other sports.