Here is what I think is video gamey (from my experience with Diablo II and Titan Quest. I tried out WoW, but it seemed to time-intensive to get to a interesting level, and the first "quests" were to simple to my test. Anyway, my experience is limited)
- A straight adventure plot. Little possibility to stray away or coming up with a clever plan to bypass some problems. The plot is always go to point X, where you talk to/kill Y. (No politics, intrigue, criminal investigation and so on)
1) The story is only there to get you into areas where you take monster. You can basically totally ignore what the people say to you and only notice the areas you have to go to.
2) Running through the wilderness and killing monster after monster.
3) Running through a building/underground passage and killing monster after monster.
(I separate this from the second point because I can see that buildings and lairs from enemies are monster-infested, but I am not certain that the "monster density" in the wilderness and the dungeon should be the same)
4) Hoarding mana potions and healing potions and constantly using them during combat (without taking any in-game time)
5) A very limited amount of abilities you get with your character class. Most the time, you just improve an existing ability, until you get access to a new one.
6) Limited tactics. Basically, tactics is just: When do I use special ability X, and the rest is target your enemies and click your left mouse button until they are all dead.
It should be clear that this "definition" of video-gamey is pretty much limited to the action oriented role playing games (not games like Neverwinter Nights).
Because honestly, the "other" type of roleplaying video game wouldn't bother me that much, because it is what D&D is now (naturally), except that you will often be able to "personalize" the story in a real D&D game a lot more (which is not limited by conflict resolution mechanic of the computer game)
Point 1) is not really a problem with the game rule, it is a limitation of computer games and goal of the game itself. A DM could always play his adventures like this, but most want, regardless what the game mechanics have to offer (but good mechanics for "social encounters", puzzles and traps can help a lot)
Point 5) Can be a problem, but D&D 4 doesn't seem to go that way. They are constantly implying a lot of customizability and special abilities.
2) und 3) are not a part of the game rule, but how the DM defines his world.
4) well, drinking potions costs time in D&D, and is often enough a suboptimal choice during combat. You don't really horde them. (You horde Wands of CLW, but they are not used during the combat.)
6) D&D is pretty tactic rich, and I think that will not change in 4th edition. Sure, in the end you still just beat on your enemy with all you got, but movement and positioning stays important.