No. Might be cooling related (I'm on my phone at so haven't actually looked at the videos).
But it's nothing to do with bed leveling. The head moves in a plane, and leaves a flat layer of plastic under the nozzle as it moves. Each layer builds on top of that. Therefore once you get past the first layer or two, the levelness of the bed is irrelevant: you're printing on top of the completely aligned layer of plastic below.
It's cooling. If you look at your video, notice how the right fan never really moves in over the print while the left one does? That's the cause.
It's a cooling issue. It looks like the fan on the right (the problem side) is fine. So I think it is simply that your bed is too hot. The default is 75C which is too hot. You will get much better results at 70C. It doesn't sound like much but it makes a diff. Most people use 60C. I usually use 60C but for very large parts I usually use 70C to keep the corners from lifting.
The reason it isn't symmetrical is because the nozzle is to the left of center so the left fan has a better angle on cooling the part.
Also the right fan is squished a bit. Look at the gap between the head and the fan on each side. It should be more like the fan on the left. You can just pry that apart with a screwdriver.
Well, that's what you call consensus I guess. 
I'll do another print with bed temp down to 70 or even 65° and maybe another print with a different fan angle.
Right now it's printing my first own design for one of my RC boats. We'll see how that goes.
Thanks for your swift responses, guys ! 
If you want to get a baseline I recommend printing this part early on so that if you have problems later with underextrusion you can reprint the same thing and see if something changed (you only need to read the first post):
http://umforum.ultimaker.com/index.php?/topic/4586-can-your-um2-printer-achieve-10mm3s-test-it-here/
Will do. I'm in the middle of a 17h print right now. Bold choice for a fourth print but things look pretty good when I left home to go to work.
SandervG posted a topic in Official news,
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calimero 0
Continued ...
Things get a little more interesting (or obvious ?) with the third video:
If you skip to the 3 minute mark, you'll notice that the "serrations" ("rings" ?) of the robot's arm don't look the same on both sides. While the right arm (left of picture) is clearly defined, the "rings" of the left arm seem somehow fuzzy. It looks like it was at bit "squished" which I assume means build plate is not level ?
What's your take ?
Thanks for you help !
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