Here's a bit of extra sauce if it helps to fully understand the issue.
"Kevin from XenForo.com" - That's just it, there is no physical "arcade.php", it doesn't exist. With XF under Apache using the .htaccess file that comes shipped with XF, both "arcade.php" and "arcade" handled by having a route for "arcade" and the request is handled correctly. When some arcade games post their scores back they explicitly post back to "arcade.php" (it is in the SWFs AS, not something that can be changed) and it shouldn't be a problem with XFs handling (in that XF's index.php is the real index page being served and then internally XF handles the route handling to determine what content to served).
To look at it another way...
These URLs go to the same page here at XF.com even though there is no physical file named "members.php" in the /community folder, just a route to "members" that is handled by XF. Clicking on either of those links brings up the XF members page as expected.
Works: http://xenforo.com/community/members
Works: http://xenforo.com/community/members.php
By contrast check the URLs below. With Nginx the URL containing the page extension is not working. You mentioned you haven't implemented the rules yet on your server so it is to be expected that it fails on your site but it should be working on CK's site.
Works: http://www.rocketslice.com/community/members
Does Not Work: http://www.rocketslice.com/community/members.php
Works: http://the-sps.org/members
Does Not Work: http://the-sps.org/members.php
Now where it gets even more fun is that it does not have to be a .php extension. For example, http://xenforo.com/community/members.mp3 also works just fine to bring up the Members page.
The problem ChemicalKicks is having with "arcade.php" is just an example of the how XF running on nginx is behaving differently for him versus when he was running Apache but the probem would not be unique to just the arcade (it would affect anything where an explicit request to {whatever}.php was being done and {whatever} was an XF route instead of a physical file).
Compounding the problem, possibly, is that CK is running XenPorta that has its own rewrite at work as well. For example, at 8WayRun.com (the creator of XenPorta) you can go to http://8wayrun.com/ or http://8wayrun.com/portal or http://8wayrun.com/portal.php and all will show the portal page as expected but on CK's site http://the-sps.org/ and http://the-sps.org/portal will work but http://the-sps.org/portal.php results in a blank page.