Just to be sure, you should reset the preferences for your app in case you have accidentally set it to always open the link in chrome rather than show the chooser dialog. Once "Always" is used to open the matching uri, it will never show the chooser.
Second, you can have as many data elements in the intent filter as your want, but it is not necessary to repeat information. You can do the same thing like this:
<data android:host="mywebsite.com"/>
<data android:scheme="http"/>
<data android:path="/map"/>
<data android:path="/animals"/>
<data android:path="/articles"/>
But note that for the path, you can just use a wildcard
<data android:path="/.*"/>
Consider adding an additional
<data android:host="www.mywebsite.com"/>
And finally you may not want to show the chooser dialog but open a specific app intent/activity directly. On your website, if you detect the android user agent, you can create a link url this way:
<a href="intent://mywebsite.com/articles#Intent;package=com.myapp;scheme=http;end;"/>
See here for more details How do I open any app from my web browser (Chrome) in Android? What do I have to do with the A Href link?
Note that with this method if the app is not installed the user will be taken to the Google Play store for the specified app package.
If you are still having problems, check your intent filter priority. http://developer.android.com/guide/topics/manifest/intent-filter-element.html