Even though there is a lot of back and forth on this topic, and the OP has probably gone for good, I'm gonna chime in...
First, I have ridden the r5 and dogma, and dogma2, and dogma65.1, and r3, and old r3sl, and r5ca etc...
As mentioned previously, the video does not depict stiffness, it depicts oscillation. the reason the bars can flex to the left so far is because they're rebounding from being pushed to the right, and the forces are stacking up. A strong enough shimmy can literally rip a frame in two (mostly old school steel, but...).
So what I believe I'm seeing is NOT shimmy, as its not shaking on its own in a complete runaway manner, but it's very close to the shimmy frequency.
The dogma is stiff, but not overly so. I always felt like it was greater than the sum of its parts. I diidnt WANT to like the dogma, but it always inspired confidence. I believe it is well damped in the head tube, possibly damped in the frame in general in torsion but not in vertical compliance. Then it avoids feeling 'dead'. IMO damped vertically = dead.
As for the test in the video being relevant to stiffness, I obviously don't agree. As for "people in the industry" using it and believing it correlates, I'm not so sure. I'd like to hear that straight from them instead of second hand. sometimes important parts are lost in translation. then again, I've met absolute idiots clinging on to myths and folklore in all levels of many, many bike companies and, well, everywhere....
+1. just because 'people in the industry' test this way, doesn't mean they're right. lots of bike reviewers know nuts about what they're testing. how many half baked reviews do you often read in bicycle mags?
I'll contend that lots of the more 'scientific' tests you see in ride, or in velonews, aren't that accurate either. yes, measuring deflections does give you a more empirical figure to compare against. but thats just the frame. a bicycle is a sum of assemblies, and a problem in a single one affects the whole system.
IMO, most modern bikes are extremely well engineered, any perceived increase/decrease in stiffness, given similar budgets and materials is likely to be less than a 5% change. Much as I hate to say it, but alot of the time it's our minds which magnify these things. the new bike you spent $5000 on is most likely going to feel better than your old one. not saying that there are NO differences, but those differences are rarely going to be able to be distinguished
FYI I am a mech engineer who does FEA testing. not on bikes, but the physics is similar. the facts don't lie. I may be starting to do FEA testing for a custom framebuilder within the next year or so, maybe I'll report back then.
for the OP's case, it's difficult to tell. so many things could be happening. if you've ruled out everything and something is still wrong, and you've checked the frame then chacnes are it would be a geometry issue.