There are two ways this is done in normal games.
- Offline games: nothing as complex as pub/sub - that's massive overkill. Instead you just use a big map / dictionary, and log named "events". Then every X frames, or Y seconds (or, usually: "every time something dies, and 1x at end of level"), you iterate across achievements and do a quick check. When the designers want a new event logged, it's trivial for a programmer to add a line of code to record it.
NB: pub/sub is a poor fit for this IME because the designers never want "when player.distance = 50". What they actually want is "when player's distance as perceived by someone watching the screen seems to have travelled past the first village, or at least 4 screen widths to the right" -- i.e. far more vague and abstract than a simple counter.
In practice, that means that the logic goes at the point where the change happens (before the event is even published), which is a poor way to use pub/sub. There are some game engines that make it easier to do a "logic goes at the point of receipt" (the "sub" part), but they're not the majority, IME.
- Online games: almost identical, except you store "counters" (int that goes up), and usually also: "deltas" (circular buffers of what's-happened frame to frame), and: "events" (complex things that happened in game that can be hard-coded into a single ID plus a fixed-size array of parameters). These are then exposed via e.g SNMP for other servers to collect at low CPU cost and asynchronously
i.e. almost the same as 1 above, except that you're careful to do two things:
- Fixed-size memory usage; and if the "reading" servers go offline for a while, achievements won in that time will need to be re-won (although you usually can have a customer support person manually go through the main system logs and work out that the achievement "probably" was won, and manually award it)
- Very low overhead; SNMP is a good standard for this, and most teams I know end up using it