They would have to be entered in the article using the "&#xxxx" syntax, which may or may not require that the article accepts HTML. If it requires HTML, you should create chess-piece templates in an admin-only template area. You can then include them using [template]Pawn[/template] etc.
As they are now, they are the raw characters. I could write some code to have the server translate all characters to entities (in fact I just tried it on your site), but it does not work as we would have hoped for chess characters. The server can translate some characters to entities, if the server has the map installed. Usually the server character maps match the corresponding RFC for the character set. The RFCs for ISO-8859-1 unfortunately do not contain chess characters.
I suspect that chess characters work on your regular forum pages only in some browsers whose makers thought it would be fun to include them, or those specific posts use the "&#xxxx" syntax directly. But the server doesn't have access to the same copy of the map that the user's browser might be using, and as I mentioned the server maps don't include the "&#xxxx" values for anything that wasn't defined in RFC.
The other option would be to ignore that the server doesn't know and to teach it. Training the server to translate individual characters is not something VaultWiki can do, as there are 65,535 possible combinations in ISO-8859-1, many of them are allowed to be customized, and that is just one of the sets that sites might be using (with some other sets having millions of combinations). Thus it is not a good focus of development time when the server already follows the standard definition of ISO.
If on the other hand, you find other characters that are defined in the RFC for ISO-8859-1 that are not working correctly in integrations, such as Greek alphabet characters, I would be happy to revisit this issue.