This was originally going to be a comment, as I'm not 100% sure of its accuracy, but here goes:
At least with the stock Gingerbread browser, every link that you click makes the browser broadcast an intent to see which apps respond saying that they can handle the link's target themselves (like when you follow a Play Store link and it asks you if you want to open it in the browser (play.google.com) or in the Play Store app). Since no apps respond the browser essentially ignores it. When you ask to open it in a new tab, the browser already knows exactly what you wantit to do with the link, so instead of querying your apps, it simply opens the link in the new tab (like opening a new tab and typing in the URL). So that's why it works when you open in a new tab, but not when you simply click the link.
As for a solution, you could try HTTP Server, AirDroid or similar apps. Once you setup the server, your target addresses should look something like http://127.0.0.1/whatever. Since this has an http:// protocol the browser recognizes this.
EDIT: To my understanding, you can also use other (potentially free) server apps, like AirDroid. When it tells you your IP address is http://xxx.xxx.xxx.xxx:abcd, you use that when you are connecting from another device, like your computer. But when you are using the same phone that you are running the server on, just go to http://127.0.0.1:abcd in your android's browser.
