In your video we can only see the passenger side of your steering, both the DL and TR ends are moving in a way they should not be moving (up/down) They should only rotate backward/forward as they have a built in misaligment so it should be safe to say both ends on the passenger side of your DL and TR are toasted.
You should also be checking your BJ's for play, if they move up/down as well they're toasted.
If you have couple of tools and measuring tape you can do this work yourself (change DL and TR). It's simple and the alignment is easy as well. You're only adjusting toe. if you know how to turn a wrench is half day job taking your time since it'll be your first time

If you're NOT doing rocks, OE steering will work with 35's but you want to at least replace what you have with something that will last. I've tried Moog and Crown and they're 100% trash, 1 year at most and you'll be replacing these parts again.. Mopar at least will last but i understand it's expensive for what it's. HD aftermarket is more expensive but you should get the piece of mind and many trouble free miles.
The Rockjock currectlink is $668 is a a simple install. Better ends than anytthing Moog does and beefier bars. This is an upgrade from the OE stuff but the tierod is not rock proof just in case.
RockJock's Currectlync steering system for 2007-2018 Jeep JK Wranglers features an alloy steel 1 1/2 Inch diameter tie rod, 1.3 Inch diameter solid forged steel drag link, larger forged, greasable tie rod ends and premium jam nuts and adjuster. This kit is completely bolt-on and includes a heavy...
www.claytonoffroad.com
For something a lot more heavy duty I like Synergy steering but it's more expensive as well. They've have been in business forever and their rod ends are simple and robust, their bars are made to last, Made in USA components.
Synergy Jeep JK / JKU Steering Kit
www.polyperformance.com
Not a fan of the aluminum steering but you have options in that camp as well and cheaper too depending on components
for example
Solid 7075 Aluminum Tie Rod And Drag Link Kit For Jeep JK Complete steering upgrade for maximum durability. Replace your entire factory steering linkage with this bulletproof 7075 aluminum kit that eliminates weak points and flex under load. Designed specifically for Jeep JK Wranglers, this...
www.ruffstuffspecialties.com
Or if on a budget OE stuff from Crown and the like is cheaper, again this is not HD at all, is OE stuff. Nothing in the OE aftermarket last as long as Mopar does, it's cheaper yes but that's all. I've tried this stuff. This is crap for a year at best, but if you need something now and cheap and you're not doing rocks this will do just fine. It came handy for me once, i'm cheap what can i say
FREE SHIPPING! Don’t Let Sloppy Steering Ruin Your Day. There's nothing like bad steering to drive you nuts. You want to go one way, and the wheel wants to go a
www.extremeterrain.com