To recompress with pixz, you'd do:

pixz -d < glibc-2.27-chromeos-x86_64.tar.xz | pixz -9 > glibc-2.27-chromeos-x86_64.tpxz

Storing the intermediate uncompressed version is unnecessary and wasterful.

pixz allows you to extract individual elements without uncompressing the archive from the start by storing an index at the end of the archive with information as to where to look for them in the compressed file.

It can only do that if it can first seed to the end of the file to get to that index, and then seek back within the archive to extract those elements wherever they're found. Which is why it can only do that when the file is a seekable file.

In curl... | pixz -x member, pixz's input is a pipe. pipes are not seekable, you can't skip to end and seek back on those.

You'd need:

pixz < glibc-2.27-chromeos-x86_64.tpxz -x member

Or

pixz -i glibc-2.27-chromeos-x86_64.tpxz -x member

For the input to be the seekable file in the current directory.

I'd agree the man page could be clarified.

The fact that pixz extracts the entire archive when asked to extract only some members when the input is non-seekable is also counterintuitive.

The rationale for pixz to do that might be that if you do it as pixz -x member | tar xf - member as opposed to just tar xf -, that still lets you extract the member even if the input is not seekable (though less efficiently in that case). That's inconsistent though with the behaviour when trying to extract members of a tar.xz archive without index.