I'm going to say yes, to your question as phrased, but with important caveats.
Yes, you need to know how to sort things in programming game development. There's lots of sorting goes on, in a wide variety of situations. No, you don't need to know the details of how all (or even many) the various sorting algorithms work, it's almost always sufficient to look it up in a reference (online or book) when you need to.
What's important is not the how and why of each algorithm, it's a deeper understanding of why some algorithms work better in some situations. It's understanding exactly which situation you have (do I need to sort in-place, can I insert items in the list cheaply). It's knowing the most common and flexible algorithms, not so much the details of how they work, but more the situations where they should not be used.
And finally, it's knowing when sorting performance is important (when you have many, many items and you need to sort them a lot) and when it's not so important (when you have just a few items, and/or you only need to sort when the list changes). In the latter case, just throw the list through quicksort. If your objects are large, then sort a list of indices to the objects rather than the objects themselves. In the last dozen or so years I've been developing professionally, I can count the number of times I've needed a more tuned or specific sorting algorithm, and it's probably less than 20.