Edit: While Horizon assigns versions internally, it looks like they are not currently used for catching concurrent client-side modifications by different users. (I previously wrote that they would cause the "losing" write to fail if it was based on an outdated version of the data, but that doesn't seem to be the case yet.)
I opened an issue against our docs to add information on this, as I'm a bit fuzzy on the detailed behavior myself: https://github.com/rethinkdb/horizon-docs/issues/50