That bold bit seems a bit off the mark though. The push there is to ensure that the GM has no meaningful say other than railroading levels of fiat.
To me it's also a matter of balancing an encounter without having to worry about the next four.
The attack roll is gone. Both monsters and PCs always hit successfully. Instead you have a power roll that determines which of your abilities are available. You can always use an ability that needed a lower roll if you roll high but not the other way around if you roll high.
Each class has some kind of class specific resource used to power their abilities in combat (usually kinda free outside combat). Those resources are gained by doing things that fit the class theme and such so you tend to get more of your resource by playing your character and being awesome. The GM ALSO has a resource called Malice, iirc it's one per player each round of combat and it can be used for a bunch of stuff in combat.
I think you're confusing your terms here. In Draw Steel, the Power roll is the stand-in for the attack roll, and is 2d10+one of your stats – your class-relevant stats will usually start at 2 and go up as you level up. It can have three different outcomes (or four counting crits), conveniently named Tier 1, 2, and 3. Attacks always do hit, but deal different damage depending on tier outcome, and can also have different special effects. For example, the Fury ability "Impaled!" has these outcomes:
≤11: 2 + M damage; M < WEAK, grabbed
12-16: 5 + M damage; M < AVERAGE, grabbed
17+: 7 + M damage; M < STRONG, grabbed
So on a bad roll, you deal 5+M (your Might score) damage, and if the enemy has Might less than your "Weak" potency they are grabbed. That's not where you want to be, but at least you didn't waste your turn. On a middling roll you deal 5+M damage and grab them if they have Might less than your Average potency. On a great roll, that's 7+Might damage and grabbing if they have Might less than your Strong potency. On a crit (natural 19-20) you get a tier 3 result and also get another action. Those intervals are the same for every ability so you'll quickly get used to them.
What you're thinking of is probably the d3 roll (for some classes, others have a fixed 2) at the start of your turn to gain resources.
Potencies are what Draw Steel uses instead of saving throws for attack riders. Your Strong potency is equal to your class's main stat (so Might for a Fury), and the Average and Weak are that -1 and -2. So in this case, a tier 1 result grabs opponents with Might less than 0, tier 2 less than 1, and tier 3 less than 2.