This is an OK method for a quick edit.
But you get a lot of color-loss. You can see in the purple in this image is gone on the scaling up.
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One suggestion would be, because the sprites are probably already paletted and use maybe 32 colors, use the magic wand (photoshop) and set the tolerance to 2 or 3. The smaller the more accurate, but the more clicks you'll have to do. Click each purple until ALL of the purple is selected. Then cut(ctrl+x) and paste (ctrl+v) into a new layer. Once each part of the spark is separated apply the Gaussian blur to each layer. Use ctrl+e to combine all the layers back into one, and save as your png or whatever.
This is my attempt. I did the first image the way I mentioned, and then did it the original way
Spoiler, click to toggle visibiltyYou can still see a couple problems. I didn't do the large canvas size like the tutorial says. So this is proof you NEED to do it. You can really tell at the bottom. But if you want the green and the blue, adding the few simple steps helps.