Electrical – Electric wiring in a kitchen island

I looked at the link you posted, personally, I think it looks a bit gimmicky and perhaps impracticable if you use it regularly. I think you would be well served with permanently built in GFCI receptacles. I would suggest that they be built into the sides of the island. (never the top) Assuming the island is fixed in position, simply run wires up from under the floor, install device boxes in the left and right side panels of your island. You can use old work plastic boxes with retainer tabs. Using the box as a template, trace the shape on your cabinet panel, cut it out with a jig saw, install the box, bring your wires up from below, wire the GFCI, done. Now you will have electrical power available from either side,and not have to worry about dirt or liquids getting into them. Good Luck

The box in your picture is called an "old work box". They still manufacture similar boxes, and they also make old work boxes with even more robust attachment methods. link to one of the many manufacturers. Link to old work bracket.