Dexos 1 is a GM-specific standard that came out a while ago (I'd guess about 10 years, but I don't have the time to look it up at the moment). As I recall, they were concerned mainly with low-temperature flowability and SAPS evel. At the time, it was a superior standard. Nowadays, pretty much any decent oil will meet the Dexos 1 specs.
The newer revision of the standard is Dexos 2, which I believe added some additional requirements for volatility (Noack and TEOST). Again, I can't look this up at the moment, but I'm pretty sure that's what changed from Dexos Gen1 to Gen2.
Group 3 refers to the base oil, which in this case would be a highly-refined crude oil that meats the non-existent standards to be called "synthetic." Neither API nor SAE define exactly was "synthetic" means, however; so you're pretty much trusting the manufacturer's reputation for Group 3 oils.
Without knowing the brand name and specific label, that's all I can say. Neither Dexos standard is considered the pinnacle of oil technology nowadays, but an oil meeting either standard will at least not be crap. If you can find out the specific oil, we can learn more about its properties.
Run-Rite has been around for a while. It doesn't do anything all that different from what a can of any decent intake cleaner will do, but it does it without having to stand there and hold the can. It's a convenience more than any sort of magic. You can do the same thing yourself with a can of CRC, Seafoam, Lucas, etc. and a helper to maintain the RPM while you're doing it.
Thank you for that oil lesson, it really helps me understand things. I'll make sure to go with the next time my wife takes it in for an oil change and ask questions, especially since it wasn't taken to a Jiffy Lube type of place, but an actual auto mechanic shop. In fact the same shop that the previous owner used exclusively, according to the maintenance records on the CarFax. Not that many shops seem to register their work with CarFax, this place does. At least this is what I'm deducing from reading a load of CarFaxes when I was looking for a car—maintenance records were somewhat rare. The shop has a good reputation.
As for Run-Rite, they had a video for that GDI kit and it seemed that it didn't do much different that a can of CRC or Seafoam. I'll stick with one of those! 👍