This is supposed to remove .php file extensions
Well, strictly speaking, this code is intended to add the .php file extension back again (in order to route the URL). (You've already "removed" it by making a request for /api/products/all.)
However, this code isn't doing what you think it's doing. This is only working on your local server because of the MultiViews line (part of mod_negotiation). The mod_rewrite code that follows is not doing anything at all, which is possibly why this is not working for you on Heroku?
If the mod_rewrite directives were allowed to run (ie. if MultiViews was disabled) then this would rewrite a request for /api/products/all to /api/products/all.php, which is clearly not correct in this example.
I don't know what other URL formats you are trying to handle, but to specifically route a URL of the form /api/products/all to /api.php/products/all using mod_rewrite, you would need something like the following instead:
RewriteEngine On
RewriteRule ^(api)/(.+) $1.php/$2 [L]
The RewriteCond directives are not required if you are only matching this specific URL.
...and the "products/all" are just read in with php
This is called additional pathname information and is managed/collected by the server and passed onto PHP in the PATH_INFO element of the $_SERVER superglobal. Whether path info is permitted at all is dependent on the server. (If not then such URLs would result in a 404.)
UPDATE#1:
...if I also have files such as example.js.php (where I use php code, but render them as javascript files) and I would like their .php to be removed so they can be accessed via example.js how would I modify the rewrite rule?
You could add an additional rule block like the following:
RewriteCond %{DOCUMENT_ROOT}/$1.$2.php -f
RewriteRule (.+)\.(js)$ $1.$2.php [L]
This intercepts all requests for .js files and rewrites the request to the corresponding .js.php file if it exists.
Alternatively, you could specify the RewriteCond directive like this:
RewriteCond %{REQUEST_FILENAME}.php -f
Note that if your .js files are also located under a URL-path that starts /api/ then this rule will need to go before the above rule that routes your api calls, in order to avoid a conflict.
UPDATE#2: You may also need to set the correct mime-type for these resources. (Whether it works or not with the wrong mime-type is browser dependent.) Since the .js URL is being internally rewritten to a PHP script (ie. .js.php) Apache will naturally serve this with a text/html mime-type (as it does for all PHP files by default). You can either make sure you are explicitly setting the correct Content-Type header from within your script, or set this in .htaccess using the Header directive (mod_headers). For example:
<FilesMatch "\.js.php$">
Header set Content-Type "application/javascript; charset=UTF-8"
</FilesMatch>
Note that this will only work on Apache 2.2.12+ (before this version it simply wasn't possible to set the Content-Type header with the Header directive).
Note also, that the "simpler" method of setting the mime-type using the T flag on the RewriteRule doesn't work in a per-directory/.htaccess context - it gets overwritten when the rewriting process starts over.
