The code I use to do this in htaccess is just

AddType application/x-httpd-php .htm .html

The code you put above does not have a dot before the htm html etc, maybe that makes a difference?

You have two lines there and it may be also that you only need to use one of those lines, depending on how your server runs php.

For web servers using PHP as apache module:

AddType application/x-httpd-php .html .htm

For web servers running PHP as CGI:

AddHandler application/x-httpd-php .html .htm

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