Just for the record, that's what I always thought too - and as a developer, for a long time I was of the opinion you really only needed general algebra for coding. (Per the article, yes, I started as a web developer.)
There's a lot of really cool - and really complicated - "math" that has little to do with number crunching though, and while you can get by perfectly fine without it, it can put things in a whole new perspective. Set theory, for example - heavy stuff, but can also put relational databases in a new light, and gives birth to relational algebra which is all about databases. Category theory turns functional programming into something that's more than just a syntax tweak for lambda functions. Every language has some basis in type theory - even dynamically typed languages. Stuff like graph theory has more direct applications, and you can even squint really hard and find uses for it in stuff that doesn't look like graphs at first - linked lists, trees, etc. Process calculi for parallel processing, queuing theory, all sorts of mathematic laws and proofs and stuff. And by one discussion - the Curry-Howard correspondence - you can even look at a well typed program as a mathematic proof.
There's so much more to math than numbers! Again, you can have a great career without knowing the foundation of a monad (or even what it is), but it can also make things so much cooler - "if it builds, ship it" becomes more of a reality than a joke!
Computer science is a very broad subject. There cant be a direct contrast of cs and web development. Web development is one of the area that involves computer software, networking, machines, protocols and many more i don't know of.
Web development is not entirely limited to css, html and a bunch of images on a website. Web developers mostly are programmers and they can code both for almost all platforms. There is no limit to what a programmer can do with machines. For instance bitcoins is implemented in c++ and has good enough algorithms to make a difference in the world.
computer scientist! bleh!!