My first approach to this is it is super cinematic and is basically Spartans murdering their way down a hill. I'd be tempted to minimize the rolls. Maybe a couple shooting rolls, some agility rolls, and some endurance rolls to get people to the bottom of the hill with a heavy narrative focus. It's just an intro not meant to be the show stealer, so why make it that.
Then, I watched it again and I realized something else. This is two things: one, it is a power fantasy, and two it is a framing device to show how this spartan team works together. They're a new team. There isn't a lot of team work. It show cases individual abilities be the guy in grey doing the ground pound, the girl in red engaging in extreme close quarters combat, and the others doing their various things. With that in mind, you take a system where weapons kill people quick, high damage and low health, then set up the scene with lots of enemies who shouldn't be able to hit the PCs but have threat in numbers. Steal the cards idea to have random big things happen to keep the PCs on their toes, and my descriptions frantic and frenetic. Then just let the players run through it and feel what their characters can do. It doesn't have to be a long fight, you are keeping them moving after all, but still let them feel strong and like the super soldiers they're meant to be.
Like the video above this is both an intro to the team, and a power fantasy. However, unlike the previous video this is a team that knows each other, and knows what they're capable of. Where thelast video showcases the individual members of the team, this one showcases a fully formed team that works together. Look how in sync they are, look at the formation, the shared reaction, and above all the confidence in smashing through the window and just watching, knowing what is going to happen.
This isn't the kind of thing you want to break up into multiple rounds to feel out characters. This is the scene you use to let the players feel super slick and bad ass in a different way. One roll, maybe two - for the group - to get things done. In particular, whatever you want to roll for staying in formation, and then a will roll (perhaps intimidation) to stay still and know what is going on. It doesn't need a lot of rolling though. It just needs the idea and characters who know each other how to do it. Let the execution be fluid. Let the players see how easy it is to succeed at htings like this because they're just that bad ass.
Like I said, these aren't the right way or the only way to do these. They're just the way I think I would try to run them. I'm still curious about how you would.