You can put me down in the meaningless distinction camp. Back in the day, it was a useful designation to separate “American” board games like Sorry, Monopoly, Scrabble, and etc from “European” board games like Catan, Ticket to Ride, Carcassonne, and etc. As a whole, though, the hobby has moved on. Today, it’s more useful to define games in terms of specific mechanics and level of interactivity, with similar games being grouped in genres. A few examples would be trick takers, deck builders, worker placement, auction games, and cube rails, though there are many more.

It still has meaning, but the lines have become a bit blurred. They used to all have more toned down art and dry themes like Castles of Burgundy, Hansa Teutonica, Tigris & Euphrates, and Medici to name a few. Now many have better visuals and themes while still maintaining the core aspects:

• Few luck elements where the board state can be read and strategic decisions made off that information. There can still be some luck, but you have ways of mitigating that luck or that luck affects all players relatively equally like board setup.
• No “take that” elements where someone loses a card or board pieces or something directly or where all players can gang up on a single player. Instead “fights” are more over who gets to a space or gets a resource first and what they have to give up in order to achieve that.
• Typically involve some sort of “engine” or build up where the decisions you made earlier in the game influence what is more valuable to you later and you see the payoff and consequences of your earlier decisions

More contemporary bgg top 100 games that I think still fit firmly in the euro category even if they have more interesting themes:

• Beyond the Sun
• Gaia Project
• On Mars

I still consider eurogames those who focus less on dice-randomness and direct conflict and more on correct decision-making and passive conflict.

I still use it as a contrast to thematic games. In a thematic game, the rules and mechanisms are in service of presenting a theme. In a euro, there is a strong emphasis on clean rules and focused mechanisms even if they are only tangentially related to the theme they are trying to represent.

I think it’s still a useful term there’s always some outliers for individual points, but a eurogame hits most of these.

• limited player interaction, and generally only indirect action.
• players aren’t eliminated
• player choice and action is the primary source of randomization.
• theme and gameplay tend to be less integrated.
• more symmetrical gameplay
• focused more on few in depth mechanics than wider variety of mechanics

It may not necessarily mean a game is European or German as much anymore, but it’s useful to denote the experience you can expect from a game.