To me, the term 'videogamey' is a perjorative term usually meaning 'childish'. I think you usually see the reference from older fans who lived through the earlier bloom of arcade video games and first generation consoles: games then were extremely simple and repetative, and were very much lacking when you looked at D&D. There was pattern memorization and... that was about it, really.
D&D on the other hand was a complex undocumented mess that required you to spend hours of non-game time on prep time: building and stocking dungeons, new monsters, new spells, new classes, new rules to cover every imaginable situation. Rules for swimming, rules for jumping, rules for hand-to-hand combat. With early D&D, it really was expected that the players and especially the GM do a fair amount of 'homework' as well. Your early adopters mostly came from two or three camps, really: the science nerds, the engineering nerds, and the computer nerds. All of whom thrived on structure, definition of minutia, and imposing rules on a chaotic world.
Honestly, many of you probably can't imagine the detail to which some of this was taken unless you pour through some early issues of Dragon or White Dwarf.
It was also a crapload of work. Most people don't like work as a rule, so the generations of gamers that came after the early adopters looked askance at all the minutia early DM's were very much into. People that were frustrated with the unclear inital rules but also were not going to put up with reading page after page of rules on how to conduct a seige, with stats for each type of seige engine used in a particular historical period.
There comes a time in every hobby when the early adopters look down on the people that come after. They were the fore-runners, they usually had to do a lot of extra work that later generations decide simply is not worth the time and effort. The latter generations invent new ways of achieving the same result that usually don't involve nearly the amount of effort, either in terms of actual work or of participation.
So, you get a split: the early adopters for whom system mastery was key, and the latter groups who have little or no need to master the system, because those same groups have already streamlined it and smoothed out all the bumps. Consecutive generations smooth out further bumps. The early adopters look down on the latter generations with, literally, that whole 'we walked to school in the snow - and liked it' attitude. They look at the simpler, clearer rules or the attitude that we simply don't need rules for fifteen different types of polearm or sword that all vary from each other primarily in weight or something, and feel this kind of slow burn.
They put in all this work and now it's just being ignored in favor of something much simpler, regardless of the fact that simpler might simply work better. Children like things that are simple because that's all that their limited minds can comprehend. Put that together with many early adopters who are convinced that D&D is for those with superior intelligence, and you're going to get a lot of accusations of simpler play being only for those who can't handle 'real D&D'.
'Videogamey' simply puts a convenient face on it, as they lump in the idea that video games spoonfeed content to children who can't handle reading rules and making the effort to spend nights in the library looking up coin weights from the fifteenth century because God knows D&D's coin weights are just completely out of whack.
