Technically, this is not a RTW :p Round The North Pole perhaps. Take a look for yourself (randomly using Chicago as start/end):
http://www.gcmap.com/mapui?P=ord-icn-vvo-uud-ovb-pee-svo-led-hel-tll-rix-arn-osl-cph-lhr-ord
Too rushed? For most people, yes it would be. Since you won't be flying, transport will take a lot of time. For some of these places, you can travel overnight by bus or train. Is that an option for you? If not, you would easily waste the better part of a day just going from one place to the next. You've listed 13 destinations and have 28-42 days, so you're probably looking at 1-2 useful days in each city. I would advice making a calendar/spreadsheet with your itinerary day by day, taking transport in consideration, to get a better idea. Have you traveled at such a high pace before?
For me, the main thing with your itinerary is: just "big" cities. Only capitals outside of Russia. In Norway for example, Oslo is really not that interesting if you're also visiting Stockholm and Copenhagen. But the fjords of Norway are one of the most amazing things on this planet. Best thing you can do is rent a car and do a road trip here (3 days would do if you're really in a rush, but more is better). Or pay for a "Norway in a nutshell" tour. Failing that, at least swap Oslo for Bergen.
Consider taking the ferry to Stockholm from outside of Tallinn (Paldiski) instead of Riga, that's usually cheaper. A few years back, I've paid as little as $8 one way for the overnight ferry!! I think they recently raised the price though.
If you don't consider London a destination, look into flying through Reykjavik. I think that would fit right into this "northern hemisphere RTW". And one way tickets from Scandinavia to the US are often cheapest going through Reykjavik (Icelandair), so you could get a layover there for free. Again, Reykjavik by itself is not a highlight, you should rent a car (or do a tour if that's your thing).
