On my android phone I have alwaysbeen able to play HTML games in chrome or other browsers by using the file:///sdcard/ directory.
If you try to open the files with the default file explorer when it opens in the web browser it is in a fake content folder and none of the images will load. On my new Galaxy Tablet trying to navigate to file:///sdcard will either search Google for the term file:///sdcard, or if there is no automatic search, says it doesn't have permissions. If I go to permissions,there is no option to give any app permissions for local files. I'm tearing my hair out trying to figure out how to access my local html files from the browser directly so they can load associated images.