FYI, using infix wildcards does not cross / boundaries, so this would only work for top-level HTML files and not those inside directories. If you use *.html *.htm instead, it should match any path that ends in that extension.
You should use {uri} instead, because {path} won’t contain the query, if there was one on the request. Also, you should remove the trailing slash in there, because the uri/path will already contain a leading slash.
You can also save a couple lines by using the single-line named matcher syntax.