There's two parts to this question (and answer), KSP and real life. I'll get KSP out of the way first.
KSP uses a simplified two-body physics model rather than full N-body physics, for performance reasons. So, each celestial body has a sphere of influence, a region in which any spacecraft are affected by its gravity and nothing else. An intercept, for the purposes of a delta-v chart, means getting close enough that you enter its sphere of influence. This is represented on the orbital map as a circular icon with the words "Mun Encounter" (or similar); leaving a sphere of influence shows up as "Mun Escape".
Note that just because you are in something's sphere of influence doesn't mean you are in a stable orbit around it. That 850dv to intercept the Mun will get you a flyby of the Mun, entering its SoI, passing it on a hyperbolic trajectory, and then exiting its SoI to return to Kerbin orbit. If you want a stable orbit, you'll need to expend additional dv circularizing. Whether this flyby is in "high" or "low" orbit depends on the precise details of your intercept burn; for bodies with atmosphere, such as Eve, you can even tune your intercept to fly through the planet's atmosphere, allowing you to aerobrake.
In real life, things are a bit fuzzier. The concept of a sphere of influence still exists, but even within something's SoI you are still affected by the gravity of other bodies. What "intercept" means will depend on the mission - if you're trying to dock with a space station, you need to get within touching distance, whereas for a flyby of another planet you just need to get close enough for the cameras.
For the purposes of your game, I would say:
- Yes, it does make sense to model travel costs using delta-v.
- If you want to distinguish between flybys and orbits, separating "delta-v to intercept" and "delta-v to enter a stable orbit after intercept" makes sense; if you assume all intercepts will be for orbits you can combine the two.
- Don't forget to give craft that can aerobrake a discount, when intercepting things with atmosphere.
- Also don't forget that there are a variety of transfer orbits you can use with different delta-v/time/return trajectory tradeoffs, including ones not mentioned on that page like the bi-elliptic transfer and cunning gravity slingshot manouvers off other planets