It's difficult to write a short answer to this question, but I will try.
Yes, the human mind is incredibly powerful at pattern matching. If you play chess for a long time, you will develop very strong "gut-feel" for a variety of positions - heuristics, if you will. These are shortcuts that your brain feels are particularly applicable to chess, and allow you to forego much calculation to arrive at the same conclusion. They are certainly incomplete, or only consider parts of the board. E.g. I have a gut feel for any two pieces placed so that a pawn could fork them; it certainly doesn't take into account the rest of the board. It is just one of hundreds of little "tools" I (subconsciously) use to make my calculations more efficient.
Now, you refer to this as rote memorisation, but I'd prefer to call it pattern matching, since the former implies a learned response, whereas my definition does not. Your actual question was whether the relative importance of this skill in rapid games leads to less time spent strategising.
I would argue that this is not necessarily the case. In my own experience, long games are dominated by extensive, deep calculations (i.e. tactics), not strategy. Strategy is definitely present, but I don't think I've ever spent hours thinking about strategy in any one game.
If you shorten the game, you are taking away the possibility of truly deep calculations; players need to rely on extremely quick (and selective) calculations, guided by their gut feelings and learned patterns. This may in fact lead to a larger percentage of their time being used to strategise, although it's difficult to say for sure. In any case, I would argue against the fact that blitz games are all about learned responses (although you absolutely must have high levels of pattern matching, to stay competitive).
To be fair, I should mention the the following:
- During a blitz game, much of the opening may literally come from rote memorisation. The set of openings is huge, but still small enough that you can learn many to this level.
- You often see a complex, 5-move exchange take place in seconds, making it seem like rote memorisation is guiding the entire thing. In fact, what's probably happening is that both players have (extremely rapidly) calculated that they would like to see this exchange through to a certain point before it began. There is no use second-guessing themselves through the exchange, so they make the moves as rapidly as possible.
- During the endgame, rote memorisation can come back into it again, though to a lesser degree than during the opening.
Again, I think it's important to note that even though these seem to suggest your initial comment was correct, I don't think it necessarily means that there's less strategy, overall. I'm sure there's less strategy - the game is much, much shorter - but there's less everything. Percentage wise, who knows.