Unfortunately, from just looking further into it. The article you provided is wrong and a combination waste and vent system cannot be used on a kitchen island sink in the configuration on the picture from fine home building and from the picture posted by gregory.
To make it work, the piping starting just after the tailpiece of the sink must be over sized compared to the tailpiece and go straight into the floor area below into a similarly oversized P-trap and horizontal pipe, which should be vented somewhere down the line. However, this also runs into another problem. For a fixture trap, the vertical height from the outlet of the sink to the trap weir of the p-trap cannot exceed 24 inches(1001.2 UPC and 1002.1 IPC). So practically, only a short stubby sink can be installed if using the combination waste and vent system, which is not going to work for a kitchen island.
This is a rarely used and fairly new system in residential, and it sounds too good to be true as well. As the piping gets clogged, the venting space can get blocked and the system can fail. But then again that would be in a clog situation, and any other wet vents could get clogged as well. I guess from less likely to more likely to clog vents you’d have dry vent, vertical wet vent, horizontal wet vent(combo waste and vent). Please read the relevant sections and see if what I’m saying makes sense.
In 910.5 from the 2021 UPC
In 915.2 from the 2021 IPC
