Don't fall in love with me yet, we only recently met
Apologies for the hiatus - a good chunk of my 'geek time' has been taken up by the Voice of Experience contest recently.
The issue of what constitutes 'theme' never seems to go away on BGG. Here are some thoughts on a classification of four basic types of theme in games. I'll illustrate each with an example from the designer I know best - Knizia.
1. Theme as decoration
This category is for truly "pasted-on" themes, where the chosen setting has nothing to do with the game play and is used purely to make the game look nice. A game belongs to this category if it would feel exactly the same rendered as an abstract.
My Knizia example is Wildlife Safari. Indeed, this game started out as an abstract, later appearing in Norse god and African safari incarnations.
2. Theme as mnemonic
These are games in which the theme provides a vocabulary that makes the game's mechanisms more intuitive to the players. However, there is little substantive connection between the theme and what players actually do in the game. Many Euros belong to this category.
My Knizia example is Ra. The Egyptian trappings make the scoring mechanisms easier to remember (rivers need a flood, monuments survive from epoch to epoch, etc.) and the game is not elegant enough to survive as an abstract. However, it's not clear who the players are supposed to represent in the game, nor does the central auction mechanism have any connection to ancient Egypt. In fact, Razzia! demonstrates that a completely different theme (the mafia) can be used to support the exact same scoring system.
3. Theme as mechanic
In this category, the game mechanics correspond directly to thematic equivalents and taken to an extreme, the games become near-simulations. This is the type of game that inspires arguments about whether the mechanisms accurately represent the situation in question, and which could not be easily ported to a different setting. Many AT and war games belong here.
Worker placement games seem like a slightly cheap way of creating a Euro game in this category. Want to design a game about underwater basket weaving? List all the activities an underwater basket weaver might engage in, put them on a central board, and innovate incrementally on how the players select from those options.
It's quite hard to find a Knizia game in this category, as it's not his design style. Maybe Lord of the Rings (which I haven't played), where a pre-existing story is rendered by leading players through a series of episodes from the narrative?
4. Theme as dynamic
In these games, the game mechanisms may be quite abstracted from the 'real-life' behaviour of the theme. But the dynamics that emerge during game play do have a strong connection to the theme. The game actually makes players feel like they are engaging in the thematic activity presented. Worker placement games often fail here, because while the individual actions are 'thematic', the overall dynamic of exclusion and blocking is not.
My Knizia example is Modern Art. The card play itself, and the varying auction types, are quite abstracted from the real-life art market. But the scoring mechanism and incentive structure encourage players to behave like (a cynical caricature of?) art dealers - talking up artworks they know to be worthless, speculating on bargains and so on.
I'm sure this analysis is not particularly original, and nor are the categories clear-cut. Many games will have elements from more than one category. To take another Knizia example, many would argue that Lost Cities belongs squarely in theme as decoration. Indeed, the basic card play and scoring system has been ported to an Irish setting. However, others have argued that the expedition theme makes the game easier to teach (theme as mnemonic) and furthermore that the risk/reward dynamics correspond to real-life expedition planning (theme as dynamic).
I do think it would be helpful to acknowledge these different meanings of theme when talking about whether or not a game is 'thematic'. Broadly speaking, I would say the first two categories of game are not thematic, while the latter two are different approaches to creating a thematic game. The 'thematic games' subdomain on BGG corresponds more to theme as mechanic than theme as dynamic.
Being more explicit about what type of theme is present in a game would also help avoid the disappointment that arises from mismatched expectations. Although I don't like it much, Panic Station is a recent example of a game that aims for theme as dynamics (paranoia) but has been heavily criticised for poor integration of theme as mechanics. I wonder if some of the many backers of Tammany Hall will be similarly disappointed to find the game is a stripped-down (and brilliant) evocation of political dynamics rather than a detailed historical representation.