Regarding Barbarian 3D, as I skipped a bit parts of the video I don't know if the comentator mentions it, but from what I read online the game is out now for iPhone/Pad and should be in 15 days for PC and Mac and in March on Android.
Anyway back to topic:
Duyumania, a DS homebrew of pretty high production quality (you can check the trailer in the linked thread:
According to the author: "Actually the idea was to make an updated Solomon's Key".
While there was no version of Solomon's key on Amiga, there are some games inspired by it, so you can easily find a way to put an entry for that
I played a few levels and found it quite nice for its kind. It is a bit different from Solomon's key as you can place blocks wherever you want among some selected location. In other words, you don't have to be next to a location to place a block there.
One funny thing was that when I tried it some musics reminded me of Amiga music. Especially, the level selection music made me think of Alfred the chicken.
One day later edit:
While looking for some information on Puzznic, I stumbled upon this page:
and therefore the whole blog: http://puzzlingiphone.wordpress.com/
which focuses on puzzle games available for iPhones and iPod touch.
I am pretty sure you can find some Amiga-inspired games among them.
I don't have an iDevice, so I won't check things myself.