That section is referring to MNPS Airspace. Of which that corner up to Iceland is a part of. It is crystal clear to me.
As for Random Routes, all flights in MNPS Airspace are random routes unless they travel the full length of a NAT Track and pass through 30W during the hours of operation of a track.
If you are "transiting" as you put it Oceanic Airspace, you must comply with the rules for that Airspace and these are set by ICAO Paris with differences. And on the many times I've been up there, we transited Shanwick which Iceland has no jurisdiction over. And always requires an Oceanic clearance.
Tthe rules say nothing of that a SLOP must be done, only that it should be done, e.g. "strongly recommended". Indeed Reykjavik CTA is inside MNPS, and keep in mind that it is one of very few areas which is defined Oceanic despite having radar. Would it be wrong to do a SLOP under radar? In that area, maybe not no but definetely not neccessary. Out of radar is a different story, but entirely up to the pilots.
The sigwx chart for that day gives moderate icing and turbulence below FL180 in a band if weather stretching from the north of Iceland to the Midlands, with jetstreams at FL290 just south of Iceland and FL350 mid way between Iceland and Scotland. Although the chart forecasts moderate turbulence and icing below FL180 I would be very surprised if the vertical development simply stopped at FL180 and there may have been cloud tops much higher if this occurred at 20 minutes after departure.
Highly doubtful that they were avoiding weather at FL390. Sure it can be cloudy, but in the mild climate in Iceland CB's rarely go above FL200 and never above FL300.
U2 usually route KEF to the UK via OSKUM RATSU UN610 STN, so if you are sure that you were over INGO VOR, it may of been due to weather avoidance.
There is actually a requirement of routing via OSKUM if crossing 010W between 64N and RATSU inclusive. So routing via ING seems very strange to me and a longer one instead of OSKUM DCT RATSU. To be honest I am surprised they don't fly further to the west and going via RATSU is a bit longer and more expensive. But then there are the winds of course to be kept in mind.