Some interesting responses so far.
It seems like those who have posted a response seem to all agree that "Monkey Diving" is not considered DIR.
As far as being a safe form of diving, the responses vary some. At one end of the spectrum, some suggest that it is certainly not ... at the other end, some suggest that the apparent risks can be mitigated be experienced people.
It's curious that the poll results show that several people believe that "Monkey Diving" is considered DIR. However, none have actively posted the reasons why they believe it is.
At least one person, Tobin, has suggested that "Monkey Diving" can be incorporated into the DIR system. He points out that many of the issues surrounding DPV diving are orthogonal to "Monkey Diving" and already have well known solutions in the DIR diving. He also presents a competing configuration that starts to look very similar to a standard singles rig.
So perhaps Tobin can elaborate more on this. Why would a DIR diver choose to scooter in such a configuration versus a standard singles rig ? Please quantify the benefits of being "streamlined/slick" that would justify the gear change.