"Thick deep bass" - Difficult to define for somone without a good frame of reference. Best I can say is that it is what it reads like; low-frequency bass with a noticibly "weighty", "thick" sound and feeling, as opposed to a "thin" one.
"Emphasized punch" - A particularly strong "thud" sensation generated by the sound wave. The same sort of pounding-in-your-chest feeling one tends to expect from a subwoofer (especially one that's cranked up too much, as most are), only of course with a headphone you mainly feel it in your ears.
"Boosted mid/upper bass" - Mid-bass and upper bass frequencies (what, 60-200 Hz or thereabouts?) are reproduced with more volume and/or punch than other frequencies. To put it another way, the headphones exaggerate the amount of bass present in the recording, as though you'd turned on bass boost or cranked up the bass frequencies on an equalizer.
Bass is usually good for games, because it makes gunshots, thuds, and explosions sound better. For instance, a gunshot on headphones with weak bass would sound more like "crack!", whereas a headphone with strong bass would emphasize the lower frequencies and produce more of a "BLAM!"
The V6 should be great for hip-hop; in fact, in your price range, it's probably THE ideal choice. It should also manage techno pretty well; the V6 tends to have overly crisp, harsh-sounding highs, but this might actually be an asset for techno.
For acoustic music, I'd actually recommend the Sennheiser HD280 Pro. However, understand that while acoustic music isn't the strong point of the V6, it is a very good headphone for its price, and I would say that it's the best fit for your requirements.