Yep - that looks really odd. I've had my PS3 and PS4 connected to a variety of TVs covering all the different technologies over the years (LCD, plasma, OLED and even CRT) and, while I have seen judder with some of these in certain low framerate games (similar to that shown in the other thread I linked to above), I've never seen anything like the behaviour shown in your example.
I think you're right in that it doesn't look similar to the usual low-framerate issue. If it was, in my experience you would see double-imaging of anything with a vertical edge (eg. building edges, lamp-posts etc) whenever you pan round, but the background in your video seems to be relatively unaffected - the problem seems to be associated with movement of the character's legs.
If you never had this problem with your old Samsung TV, then that proves it's not an issue with the game itself or console and probably not the HDMI cable, so it's hard to know what to suggest, especially if you've already tried playing with the TV's settings and gaming both with and without game mode. The usual suggestions for any TV-troubleshooting would be to check for the latest TV firmware and do a factory reset to start with. I can't see it helping in this case, but you've got nothing to lose and it would be the first thing any helpline would suggest anyway. Resetting the TV and starting from default settings can sometimes be helpful when trouble-shooting.
Have you tried playing with the motion interpolation settings ? It's not normally advised for gaming as it introduces latency/lag (it's usually disabled in game mode as a result) but lag doesn't tend to be an issue with a lot of the games I play and I found in the past that turning it on a low setting can sometimes smooth out motion issues for any problematic games. It could equally make things worse, but it's worth experimenting.
I would post in the
LG TVs Forum to see if anyone else is having gaming issues with your TV.