How does 'such as' mean 'of a kind that; like'?

This is a different "such as" and it is spoken differently. Punctuation that reflects how this one is spoken: "such, as...".

As Dan Bron says, "of the type which". Or "of a kind|sort that..."

There, "as" is like "that".

The fracture of the bone was such, as should be attended to immediately.

The fracture of the bone was of a sort that should be attended to immediately.

P.S. In response to the comment:

The vertical bar | is a symbol for 'or' indicating possible variants.

The comma indicates the natural syntactic pause that would occur here because "such" is a predicate nominative|nominal in this sentence and is therefore an element of the independent|matrix clause ; "as" introduces a dependent clause that modifies 'such'.