Can the kitchen sink waste pipe run from where it comes out of the concrete slab to the sink by running horizontally under the cabinet floor?

Horizontal - no.

No drain line is EVER horizontal. Unless someone was an idiot and should not have been plumbing....

Perfectly acceptable to run at an appropriate slope, however. 1/4" per foot (or 2%) is the standard minimum slope for small drain lines like this.

How will you handle the venting? That is a complex process for island sinks, and if it was a peninsula before probably not arranged for. You mention having a "wall behind" - can your vent run through that (is your island not an island in the usual sense?)

There are ways far less drastic than a jackhammer to get into concrete and rearrange plumbing.

You picture leaves a lot of information out, but assuming that you're putting in a standard double-bowl sink, and that the hole in the floor of the cabinet is now located over the existing drain line:

I'd suggest that you simply run your two lines horizontally from the bowl drains from right to left, then turn up, put in your trap, then run to the drain in the floor. (Note: all directions oriented as we're looking at the picture you posted. Note 2: "horizontally" means with the appropriate 1/4" per foot of slope).

To hide the plumbing (assuming you don't want to see it right at the front of the cabinet when you open the door), make a removable wood insert out of furniture grade plywood. This will have to be removable so you can access the pipes for any future plumbing changes, leak fixes, etc.

It would look something like this top view:

 D W
 | W
 P W
 | WWWWWWWWWWWWWW
 +-----B------B W

D = floor drain
P = P-trap
B = Bowl drain
W = plywood vanity panel