They knock down giant death icicle before it can kill somebody

But it was so long I felt like sideways would have cut it off!

There is never a reason for a vertical orientation. Even if you are able to capture more detail by holding the phone vertically, you lose all that detail when you upload it to YouTube and they convert it to the letterbox video you see.

If they'd kept the camera horizontal, we'd have ended up with the same vertical resolution as in the YouTube video. We would just have had lots more footage of the whole frame.

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Icicles form because they can radiate the heat of slowly running water outwards to the air and that lets the water form ice on the ice already present. This means they aren't really holding on very well up above to whatever they're frozen off of. Unlike an ice cube in your freezer which forms outward in and all the ice can come together in a mostly closed chamber, the icicle is slowly forming inward out and doesn't have the benefit of having time to let the lattice form uniformly among all of its component water molecules. It's pieceful not peaceful in its creation.

So, shearing it with a small force is a lot easier than if it were made all at once like an ice cube because it's more disorganized. Combined with having to support its own weight through tension, you should be able to crack most icicles off pretty easy regardless of their size.

I wouldn't lean out a window to do it. I wouldn't stand anywhere underneath as it can come apart on the way down. And assume that anything underneath you can be potentially crushed if it tumbles in mid-air. So, be really safe doing this. Also, it's possible that more of your gutter/eaves are involved inside of the core of the icicle than you think, so be sure your pushing isn't just leveraging the edge of your roof apart instead of just the ice.

The guys upstairs tapped the bottom with a long ice scraper we have for our building (Long pole like a shovel but a flat head for scraping up ice). I think a shovel would work just fine. It was really just the two taps you see in the video that brought it down.