Try changing the condition to only fire the rules for your pages
RewriteEngine On
RewriteCond %{REQUEST_URI} \.(php|html?)$ [NC]
RewriteRule !^page/ page%{REQUEST_URI} [L,NC]
This is easier because you won't have to worry about all the different file types that could get wrongly redirected with your rule. To answer what's breaking your existing rule you would have to share your site's directory structure and the files' location.