Form cues definitely aren't universal, it's more about applying them to the right lifter and situation.
Taking the slack out the bar stops people jerking the bar, which with heavier weights is never a good thing. By taking the slack out of the bar you physically cannot jerk it. Normally people who jerk the bar start off with a loose set up and quite often have a slight bend in the arms, too. If you have a tight enough set up you can't jerk the bar. This happens more on your first video. In an ideal world you should be able to explode at the start, but not jerk the bar. I can't see how this is possible without pulling the slack out of it first.
Also, "leaning back slightly" is great if you start off with your weight forward or pull the bar with your weight on your toes. In fact in this case i'm not sure any other cue would resolve it. Some people, and beginners especially, drive with the middle/balls of their feet when they first attempt to dead lift. You'll even see the heels LIFT on some occasions. In this case I wouldn't say lean back slightly, i say lean back hard, and will often get them to remove their shoes, too (almost always happens with beginners who constantly wear shoes with a big heel lift). I use this cue regularly with great success. Quite often this, and taking the slack out of the bar, as well as getting a better arch, are all one in the same - they don't arch so they're not tight then jerk the bar and weight shifts forward. You can then pull on the bar to get tight, get a better arch, and lean back on your heels. A lot of beginners don't know what it means to dig the heels in or get their weight on their heels, in which case you then have to ask them to "lean" (because "weight on heels" means nothing).
I genuinely don't understand how you can achieve maximum tightness without pulling on the bar. I did read the article (and enjoyed it) and note that in the set up steps you grab the bar, thereafter you "bring your chest up and shoulders back".... Is this not "pulling the slack out of the bar" ?
And if you have someone who gets pretty much everything else right but, when getting to a challenging weight shoots the hips up and pretty much does a Good morning with the bar in the hands, then "pushing the ground away" will almost always create more drive from the legs and get the hips and shoulders moving together as they should (if the set up is right, it will not make them squat the weight up).
Anyway, one of the biggest issues I see with your lift is the arch, or lack thereof. You have a much better lower back position in the first video. It does seem like you purposely attempt to "arch" but, actually just move your hips down instead, which is quite common. I think Rip (or it may have been Dan John) wrote an article recently on this specifically. It can be a case of just not really knowing how to arch your lower back hard, in which case I suggest things like RDL's to teach it. It may also be a flexibility thing, in which case, elevating the bar would improve lower back position whilst you get more mobile, and it may also be a technique thing.
I think it could be technique just based on the video with lighter weights but, it's hard to tell.
If you jerk the bar and don't arch hard enough then i'm afraid my advice is to use the bar to pull your chest up and arch your back harder (which will also take the slack out of the bar).
Also, noting that you're doing Sumo style, which i'm actually a big fan of - Can't tell if you're doing it but the one main difference in technique with Sumo's is to spread the floor apart/push the knees out. Do this hard, right from the start. This will emphasise the hips/glutes and possibly stop a lot of what you have noted yourself that's going on (hips coming up and back rounding).
In short and as a basic summary - get in close to bar (some people, for sumo, say get "under the bar"), grab the bar, pull your chest up, arch, spread the knees, big belly, and rip it up. BUT, whilst ripping it up like any normal pull, really spread those knees out hard. And, pull "back".... "Chest back knees out"...