Some people play games like others "sound bathe". Sound bathers have music playing but don't really pay attention, don't really LISTEN. They're not particularly interested in exactly what they're "listening" to, and they're not putting effort into it. Some people play games the same way, especially video games, where you're often not playing against anyone and can resort repeatedly to save games when you fail (die). In tabletop games, you often lose when you play this way, except perhaps in family/party games.
In many Euro-style tabletop games (and let's realize that this is such a large category that there are always many exceptions to any generalization), players WANT just a few choices, and then the play of the game revolves around which choice to make. The "best" choice depends on the situation, and the better players recognize which is the best choice in given circumstances, though generally there is no choice that will always work out best in a given situation.
In other games, including many "old" games and some of the new ones, there are many choices, and one of the skills is seeing all the possibly-good choices in a situation. Better players will not only see those additional choices, they may be skilled in influencing the course of the game so that those choices are available when they next have an opportunity to do something.
A sure way to spot this point of view is the gamer who plays a game once, then criticizes it for poor play balance or too few choices. While the game may indeed have those characteristics, it can also be the case that the player has assumed he's recognized all the choices, and all the balance possibilities, the first time he played.
I recall a young player at the WBC Britannia tournament (his first Brit game) who, when he finished, said he couldn't see how he could have done anything differently (no, he wasn't near winning). It was only after some expert players talked with him a while that he realized there were large choices he hadn't seen, and also, that even small choices made a difference in the long term. Perhaps he wasn't accustomed to games that did not reveal the choices immediately.
We have an essential difference:
"It's important but I haven't figured it out yet."
I haven't even realized it's important."
So the expectation in those Euros that are essentially "family games on steroids" (some are not) is that the first statement is the typical situation after one play, yet in many strategy games there will be a strong element of the second after one play.
Perhaps this is a reason (not a sufficient reason or necessary reason) why there is the emphasis on multiple ways to win in Euro games: so that the players will easily see at least one way to win at first playing.
I'll take an example from my own experience. Here's a comment I ran across about old Britannia. "Innovative, but only interesting once. After that, it's just rolling dice for 6 long hours, very boring. Green is horrible. Purple is a one shot wonder also." Here's a person who thinks he can see all possible strategies the first time he plays a game. Is that because he plays simple (shallow?) games? This player clearly didn't have a clue about many of the strategies in the game. I'm curious if he wondered what the people who've played 500 times were doing? Just rolling dice? I suppose he didn't know how intensely the game is played, how (as Tom Vasel says in his review, it "may satisfy the itch in players looking for a deeper encounter, an epic game that is all about the experience.").
Rather than consider the possibility that he'd missed something, the commenter dismissed the game. (Btw, there are lots of perfectly reasonable reasons why some people do not like Britannia, e.g. the length, the dice rolling, the "scripting", the need to plan well ahead. Poor play balance is not one of them, clearly.) This is the kind of comment I'd expect from a "shallow" player, perhaps someone who plays shallow games, though maybe just someone who doesn't easily see strategic possibilities in this kind of game.
There are a great many players of this kind nowadays, which may be one reason so many games are only played a few times: either they are shallow, so there isn't much there, or the "shallow" player isn't going to play any game many times because either he gets it easily and exhausts the possibilities, or he doesn't get it at all.
Video games are very often of the first variety, where the strategies are clear pretty quickly, in fact, video game designers work hard to make such games accessible to as many players as possible. Video games are often more non-competitive entertainment than competition, and people don't want to be frustrated by their entertainment. Video games are fundamentally different in one respect: you can (usually) experiment many times to find a best strategy, because you can go back to your save game and try again. When you play a board or card game against other people, failed experiments become losses. (You can't "lose" a traditional one-player video game, can you?)
There are certainly many deeper video games as well, but they are not the norm.
I suppose you could dub this the "shallow play syndrome". It's fairly obviously related to the "cult of the new" syndrome. While it doesn't matter to me if people play that way, it's annoying when they don't recognize that that is what they are doing, they ought to adjust their reviewing accordingly.
Many tabletop game designers try to get rid of "analysis paralysis", too many choices that cause the player to think too much and take too long. Yet some players LIKE lots of choices, and they are often the people drawn to a game like Britannia and some other wargames.
At a local tabletop game club we have one player who simply doesn't like games that require a lot of decisions at the same time. So she doesn't care for typical wargames. She plays tabletop games as much for the company as for the games, and wants to limit the strain involved.. Yet in the games she does like, she's clearly a thinker and planner, definitely a person who wants to use her brain, and I have a great deal of respect for her (face it, some gamers do not like to think much).
She is definitely not a "game bather" in the sense of "sound bather". She's not a Euro gamer per se, as she doesn't mind competition and doesn't mind hindering other players. She's my most valuable playtester *because* her objectives are different from most. But the point here is, she is more comfortable with the first kind of game I've been talking about. (Yes, she plays video games, but often the ones that require a lot of thinking.)
There are just a lot of ways for people to approach games.