I watched a Global Testfire video on Youtube and it made me feel dizzy as well. However I don't think the issue is the shaky camera, but instead the garish colour scheme.
The reason you get warnings when you boot up consoles warning about the possibility of seizures is because some people suffer from Epilepsy thats triggered by flashing lights (Photosensitive Epilepsy). Flashing bright colours can also trigger it, especially when watching TV or playing certain games that move too fast or are too flickery. On Splatoon, the colours are bright orange and purple, and when combined with the quick movement of the camera (plus the minor graphical glitches) it appears as patches of flashing colours, which can cause a seizure.
Even people who don't suffer from Photosensitive Epilepsy can get dizziness and headaches from such stimuli. One case is the banned Pokemon Episode "Electric Soldier Porygon", where some kids with no previous record of Epilepsy or Seizures suffered them after watching the scene with repeated flashing colours (the episode was only shown once in Japan, and never shown again). Likewise, a lot of people suffer headaches when playing older Atari 2600 games where there is a horrific amount of flicker due to the limited hardware.
In addition the industry now uses equipment that tests a game to see if it has a risk of causing seizures. Wipeout HD notably failed this at first due to it's original Zone mode having a track with pulsing colours, acting as a graphic equaliser for the music. This was changed in the final version so the equaliser effect was much more subtle.
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