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I love this, it's a very clever and funny way to solve the problem. Makes me think about how there are infinite routes from A to B, some more scenic and whimsical than others.. as well as all the people I've met along the way who would be so pissed and pedantic about how this isn't a "real solution" LOL
A shorter solution is possible with an ordered list (<ol>) if we're willing to ignore the untidy output:

  li:nth-child(3n), li:nth-child(5n) { list-style: none }
  li:nth-child(3n)::before { content: "Fizz" }
  li:nth-child(5n)::after { content: "Buzz" }
Example: https://susam.net/code/web/css-fizz-buzz-ol.html

  $ curl -sS https://susam.net/code/web/css-fizz-buzz-ol.html | sed -n '/none/,/after/p' |  tr -d '[:space:]' 
  li:nth-child(3n),li:nth-child(5n){list-style:none}li:nth-child(3n)::before{content:"Fizz"}li:nth-child(5n)::after{content:"Buzz"}
  $ curl -sS https://susam.net/code/web/css-fizz-buzz-ol.html | sed -n '/none/,/after/p' |  tr -d '[:space:]' | wc -c
  129
But I don't quite like how misaligned the numbers and the words look in this version. Correcting that would call for extra code that would cancel out the characters saved.
Ignoring the size of the HTML in addition to the CSS, it’s fun, but not really fair when talking about code golf. Beyond a few numbers, you need to include some JavaScript and generating a million list elements. But those bytes count …
145 using P instead of li.

<style> p{counter-increment:n} p:not(:nth-child(5n)):before{content:counter(n)} p:nth-child(3n):before{content:"Fizz"} p:nth-child(5n):after{content:"Buzz"} </style><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p><p>

To nitpick a bit, I'd say there is something that is "placed outside the stylesheet".

Now, arguably it's not a "number or word that appears in the output", that's true, but it is a part of the logic of FizzBuzz. It's the fact that there are 100 and exactly 100 <li> elements in the HTML part.

I mean, it wouldn't be a correct FizzBuzz without precisely that HTML. Having exactly 100 <li> elements is implementing the part of the logic that a. loops, and b. stops at 100.

But of course this is just nitpicking, as I said ;)

104 :nth-child(3n){list-style:"Fizz"}:nth-child(5n){list-style:"Buzz"}:nth-child(15n){list-style:"FizzBuzz"}

data:text/html,<style>:nth-child(3n){list-style:"Fizz"}:nth-child(5n){list-style:"Buzz"}:nth-child(15n){list-style:"FizzBuzz"}</style><ol id=o><script>o.innerHTML='<li>'.repeat(99)</script>

Am I the only one here who's never seen CSS counters before? Interesting feature, what are they useful for practically?