Bored Zone is run by one person, Marc Le Masson, and messages come straight to him rather than to a support queue. Use the form on this page — only the message itself is required — and expect a reply within a few days if you leave an email address.
The quickest route is the form on this page. Pick what the message is about and, if it is about one game, which one; a name and an email address are optional, and the email is only used to reply.
Every game page also has a link under its guide that opens this form with that game already chosen. If the form will not send, the contact details on marclemasson.co.uk reach the same person.
Anything, but these in particular are genuinely useful and do get acted on.
For a bug, the game and the device you were using is usually enough to find it. If the board itself looked wrong, a screenshot is worth a great deal — the board is generated on your own device and is not recorded anywhere, so without one there may be no way to see what you saw. The form cannot carry pictures, so leave an email address and say you have one, and the reply will ask for it.
A small collection of free browser games, built as a hobby project. No accounts, no downloads, and scores kept on your own device rather than on a server. There is more about how it works, and how the puzzles are kept fair, on the about page.
The contact form needs JavaScript. Without it, the details on marclemasson.co.uk reach the same person.