Any bike can do a round the world trip and this has been proven as alot of people have taken Honda's Cub 50 around the world with no problems at all. Why you would want to do it on that bike i dont know.
My opinions on the bikes are
GS800, expensive for the bike, then you have to pay over the odds for extras which just means less money to spend on the travelling part which is the part you are suppose to enjoy the most. New bike meaning you have to buy new or newly new also no other extras apart from BMW's at the moment so your kind of cornered on that. New bike so hasnt been proven as of yet in long term use. Plus side you have a twin cylinder which will cruise alot easier and the engine should be less stressed therefore less chance of going wrong.
The Dakar: A good bike in its own right and has been proven well on these types of trips but ive heard alot of storys about electrical problems going wrong or massive engine faults happening in the middle of no where. Very rare the massive problems i know but i wouldnt like to be stuck in no mans land with a bike that will not go. On the plus side you can buy them second hand and alot are moded up with the kit like panniers, topbox,screen etc that you would need for touring also if problems do arise second hand parts should be able to be bought cheaper than new ones.
The new tenere: Looks nice should be able to handle most/all of what you throw at it, but its a new bike and waiting lists are high at the moment, + being new its on the expensive side of things (i call expensive anything more than a tenner, i am a student). Not alot of choice at the moment on the side of extras for the bike as its new + the yamaha extras do seem quite highly priced like the GS800's. Plus side its been designed purely with your type of trip in mind, semi built in crash protectors and others.
XT660R. If you modded an old XT660R up with a offtheroad large 28ltr fuel tank it would be very near to the tenere but at near half the price at a guess. Its been proven by many people to be able to do this trip, its been about so parts are easy to find, massive range of extras to choice from etc etc. Down side is it needs moded up and the price of the offtheroad tank being about 900E or so is quiet steep, some find the vibes at 70mph+ annoying, short screen not good for touring anda few others.
Also depending on what you count as being bad off roading? When loaded up a bike can only do a certain amount off roading, and in the end there is always a limit. So choice your route around what you think the bike can take not the bike around the routes. I know this can be hard when you have never been in a country but you know what i mean.
Choice is yours, i would say try each out on a demo ride and see how you get on if you can get a demo ride.