I played Amber and it works fine if your DM thinks visually and is combat experienced and you are only doing physical combat ( tell me which continuum of stellar correlations will get my spell to work freely.) so you have a well defined arena of conflict .... etc etc... the rest is why we have dice and rules.
LS are you playing the right game? Amber is indeed awesome.
4E can handle the in-game situation having an impact on resolution. I think it's actually well suited for that sort of play - there are lots of tools to aid you.
The problem is that it's easy to forget about it when you have all these interacting mechanics that
don't rely on the in-game situation. When you stop thinking about the in-game situation - and once again, that's easy to do, because the mechanics don't care about it - immersion suffers.
That's why people say it feels like a boardgame. The fact that you're fighting an ooze matters as much as the paint job on your hotel on Boardwalk when it comes to resolving actions. (A better analogy might be that the hotel is actually a casino - "Yeah, so what, it's still 400 bucks rent." The fact that it's a casino has nothing to do with how the game will play out and can easily be ignored or forgotten.)
If it does matter, though...
"I jump up on the table to get away from the ooze."
"Haw haw, it stretches itself into a long column and slaps you. Your skin burns and you take 7 points of acid damage."
"It's stretched into a long column? I cut it at the base with my sword, hoping to make it sploosh down into a pool."
"Nice, if you hit, it'll be prone."
"Oh, you know what, I'll use Tide of Iron - as it falls I'll slap it with my shield."
"Okay, it'll be prone in whatever square you push it into, if you hit."
Nothing hard about that! If you can do that - if you have to do that - then you're going to be constantly engaged with the in-game situation and all the little details. When you're thinking about all the little details of the game world, guess what happens - immersion.