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Since your question is about an Illustrator tutorial, and Inkscape and Illustrator can be quite different, I moved it over to this board.
In Inkscape, clipping and masking are 2 similar, but different things. I looked up what a dribble logo looks like, and just to make sure we're on the same page, it's a pink basketball, right?
I don't see any reason to use either clipping or masking to draw that logo. From what I understand from that tutorial, they are using the Illustrator clipmask feature as some kind of a shortcut to using booleans or path operations (as they are called in Inkscape). Inkscape can't really do anything like that. At least not the behavior that you see on the Illustrator canvas in the tutorial.
While you could use clipping to create such an image, I would consider that technique not to be the best way to create a logo or icon. That's because, at least in Inkscape, the clipped or masked portion of drawings aren't really cut off. Essentially, they are hidden. So your resulting file would have hidden contents. That could cause all kind of problems, depending on how you end up using that file. I always strive to create the leanest, meanest vector file, which contains only what's necessary, and nothing else.
However, if you want to draw it that way in Inkscape, here's how I would do it (although again, I would never do it that way).
1 -- Draw all the circles, right on top of each other, overlapping and everything
2 -- Give them all the right colors and stroke widths
3 -- Duplicate the main circle
4 -- Select everything
5 -- Object menu > Clip > Set
6 -- You might want to select all, and group, to make sure all the separate parts stay together when you move the image