As far as the internet is often concerned, I'd generally agree with this. However, I don't think "casual" represents only time available/time played. There's also an attitude/preference in gameplay style. What do I mean by gameplay style?
Let's Play Scrabble!
Casual gamer: looks at their letters and casually spells out any common words they know/see. Not too much thought put into it or highest scores possible. May get bored before the game is finished.
hardcoe gamer: pulls out 2 dictionaries (may also debate which dictionaries are "valid" and how long one can take per turn), tries to use a word that maximizes potential points every turn, gets a little annoyed if game is not finished after a certain point.
...While the above are of course generalizations (and just imo), the point is that it's not always just about time spent.
imo hardcoe gamers are obsessive gamers, whether they obsess in smaller time increments or in larger ones. They obsess over numbers, over rule and combat mechanics, over roleplaying elements/lore, over "the best" strategies, the fastest, the most damage, how many different ways one can achieve the same goal, who the best character/party is, what the best unit is, or whatever else floats one's personal boat.
Casual gamers may care about those things to, but often to a much lesser degree. They're less likely, imo, to play the same game over and over for months/years, instead moving on to the next game fairly rapidly.
My husband is "hardcoe" in terms of hours spent, I suppose. And he's also liked very few games over the past 2 decades (he's picky). But despite his hundreds (maybe 1000's) of hours put into Borderlands series (and Tombraiders, Doom, and a couple others), I'd still call him a casual gamer, because 1-he doesn't want to "think" while playing a game (and he hates steep learning curves) and 2-he never goes into the same obsession mode over a game that I consider hardcoe. Doesn't care about collecting. Doesn't care about story at all. Doesn't care or even think about achieving many game-type goals, whether in-game or self-motivated. In other words, he never pulls out a dictionary. ... but he doesn't like AngryBirds, either.