When an interval closes, the chronometer sends that run to the site's daily board: the click count, the elapsed time, the interval it was run on, and statistics describing the spacing of the presses. It sends no identifier of any kind.
The board keeps only the resulting rate, the interval id and the date, in a store that expires every entry after four days. There is no name attached, no cookie, no visitor id and no ordering that could be walked back to a person — one number per run, in a pile with everyone else's.
The gap statistics exist for one purpose: telling a hand apart from an autoclicker, which is what keeps the board readable. They are checked when the run arrives and are never stored.
To stop taking part, tick Keep my results private on the chronometer. The preference is stored in this browser, the board readout keeps working, and nothing further is sent.
Submissions are rate-limited per network address to keep the board from being flooded. That counter is a salted one-way hash, is not readable as an address, and expires daily. The address itself is never written down.