I am trying to figure out why I could not define the 2d Array in the asList() method like you might a normal Array.
We cannot answer why what you tried did not work when you do not tell us what you tried.  I suppose what you really want to know, however, is how to generate a List<String[]> via Arrays.asList() by passing the individual elements, instead of first constructing a 2D array.  That would be this:
public final List<String[]> pockets = Arrays.asList(
        new String[]{"STATUS CHANGERS", "RUNES", "KEY ITEMS", "TROPHIES"},
        new String[]{"POTION", "SUPER POTION", "FULL HEAL"},
        new String[]{"ARMOR+","ATTACK+","EXP+","HEALTH+", "DISPELL+"},
        new String[]{"QUEST ITEMS","STORY ITEMS","JOURNAL"},
        new String[]{"TROPHIES"}
    );
Note in particular that Java has no array literals, only array initializers (which can be associated with array declarations), and array constructors, such as in the above code.  I speculate that in your attempt(s), you omitted the new String[] bits that make those constructors.  Those bits are necessary to specify the element type of the arrays, if for no other reason.
Also, I know there has to be a Java subclass to import or a more semantic approach.
I've no idea what you mean.  You're already using class java.util.Array to perform the construction, and you're building a java.util.List.  I guess for most purposes I'd recommend using a List of Lists (List<List<String>>) and avoiding arrays altogether, but I can't be sure whether that would be suitable for your purposes.