If you're calling a sorting algorithm, you should still know about the efficiency of that sorting algorithm takes so you can make a choice between sorting an array or indexing using a data structure (which data structure).

Web is just a UI to layer software that _does something_, algorithms are a way to get that something done. Have you ever needed to understand why e.g., a SQL JOIN is taking too long? That's an example where algorithms matter (in selecting the index type, knowing whether to use a join between two tables or to denormalize etc...)

Knowing how to do your own memory management and knowing Objective C is great and valuable, but if mobile/Mac desktop application development were to become less valuable and more commodity (right now, I don't think it will happen-- but I can't predict the market), will you be able to apply these skills to (say) working on more complex C and C++ software such as a web browser?