This seems to make even less sense in Chat than it does on the normal site.
The rationale for having it on Q&A is that readers who aren't asking or answering the question might stumble across it and have their lives ruined by exposure to surprise events in the topic of discussion.
In chat, there's a list of people viewing the discussion at any given point in time. If you're discussing a topic that several of them don't want to see details on, they have three choices:
- Ignore your messages (using the "ignore" feature).
- Leave the room.
- Ask you to take your discussion into a separate room.
Note that only one of these requires action on your part as the author of the spoiler-laden messages. If there was support for marked spoilers in chat, that would also require action on your part - other users can't force your posts to be spoilered (although this would be an interesting variation on "ignore").
If you're conscientious enough to mark your spoilers, why not be conscientious enough to just spin off a separate room where you can talk freely without trying to guess before posting each message if it reveals something the others won't want to see?
This goes for any sensitive topic, not just plot details. If the topic of your discussion is making the folks in a room uncomfortable, take it elsewhere.
Disclaimer: I pretty much loathe the idea of hidden spoilers in general.