Yes, this is legal.
No, it's not a maul (and it wouldn't matter if it were).
The requirements that you've listed are the conditions under which an attempted tackle becomes a completed tackle.
When you attempt to tackle someone, you're required to do so safely but it's not a requirement that you do so successfully - otherwise missing a tackle would be illegal.
The rules you've listed above aren't there to say that it's the right way to tackle, they're there to say that when when these conditions are met then the tackle is over and a new set of rules apply to both players (ball-carrier must release the ball, tackler must release the player and roll away).
In the scenario you've shown what's effectively happening is that a tackle is being attempted but play ends before the tackle is completed. At this point, what is/isn't a tackle becomes irrelevant.
Picking up a player?
Legal, provided that the tackler returns the ball-carrier to ground safely.
(edit: after taking another look at the clip, the tackler could be deemed to have broken the rules here by just throwing the player to the ground. It's a marginal case but if the ref thought it was fine, then it was fine)
Not a maul?
As you've listed above, a maul "consists of a ball-carrier and at least one player from each team". As there's no other player from the ball-carriers team then this can't be a maul.
The ref can't really call maul instantly, as all players must be bound together (rather than just holding) the ref will allow some time for it to be established that players are firmly bound.
Sideways movement of a maul isn't illegal, but there must also be forward movement. The ball carrying team will be given time to remedy this, and failing that be given time to play the ball.
If this had been a maul, it's completely legal for a defending team to push a maul into touch. Once this happens, play ends and the ball carrying team is deemed to have taken the ball into touch.
You can see from points 1 & 2 that carrying a player in to touch generally just happens too quickly for maul rules to apply and can see from point 3 why it wouldn't matter.
None of the maul conditions make this an "an illegal defence". In all these scenarios, the onus is on the ball-carrying team to keep the ball playable and they lose possession if they can't. How could it be an illegal defence if it's the other team that's breaking the rules?