We'd all love a fantasy game with a storyline that keeps people going for hours,, unfortunately we haven't quite got there yet though there are some options other than muds and browser games, though if you want lotr games those might still be your best bet.
one of the best I can think of is King of dragon pass on Ios, (sadly the android port isn't accessible).
I'm not sure if you'd call this an rpg, resource management game, interactive story or all of the above, but however you cut it, its a truly amazing game.
You take charge of a tribe of people with a Viking like culture in a world of gods and spirits. gAmeplay involves making decisions and also managing your tribe's resources, and can vary from sending diplomatic missions to other tribes to gain their support, to raiding, to fighting off enemy attacks, or making decisions about your farm or trade.
There are also in game events which occur like interactive stories.
What is particularly amazing is that all your clan aren't equal, and your ring of advisers or clan rulers have their own opinions, strengths and weaknesses.
It's a complex game to learn, but well worth the time and effort and is one I have indeed played for hours.
Another option which might or might not be too similar to the browser games you mention are gamebooks, I'm particularly thinking here of books like those on the choiceofgames website.
these are interactive stories where you make choices on behalf of your character. What is especially notable for these is that your character has stats that influence their ability to succeed at things but each stat is usually a combination of a percentage choices, for example I can think of one game where you have a stat of finesse/brutality. So if you take a straight forward approach to fighting your brutality stat goes up, where as you make choices more based on evasion and swiftness approach your finesse goes up.
This is fine, however you will find occasions, say where your dodging an incoming blow or trying to knock and enemy's weapon out of their hand where you will need one stat or the other, and your choices will dictate your success and failure.
it's not always about fighting either, for example I can think of one game where you have an honesty/duplicity stat. Honesty is all very well for making yourself believed when telling the truth, but what do you do when you need! to fabricate story in a hurry?
I can strongly recommend these, they are browser based, though can be played on Ios, but are very different from your standard click attack to fight type browser game.
Also in the matter of gamebooks there are the ffproject, project aon and chronicles of arborell if you want a more traditional story with the usual choices and diece based combat, ---- though don't under estimate these (there are some very long and complex adventures on both sites to keep you going).
This is about all I can think of in terms of fantasy and story line.
of course we have a few audio rpgs now, Entombed for a basic dungeon crawl with lots of tactical monster killing, Manamon which is very much like audio pokemon, and paladin of the sky which is more a mainstream console rpg with a rather odd story and combat mechanics, or the adventure to fate games on Ios which are more like ractical combat outings, so if you wanted something slightly outside the story based medieval fantasy genre you could try those.
hth.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)