Can Initramfs Image Use Compression Format Other Than Gzip?

It is also possible to decompress it using standard shell-script + gzip, if you don't have, or want to use openssl or other tools.
The trick is to prepend the gzip magic number and compress method to the actual data from zlib.compress:

printf "\x1f\x8b\x08\x00\x00\x00\x00\x00" |cat - /tmp/data |gzip -dc >/tmp/out

Edits:
@d0sboots commented: For RAW Deflate data, you need to add 2 more null bytes:
→ "\x1f\x8b\x08\x00\x00\x00\x00\x00\x00\x00"

This Q on SO gives more information about this approach. An answer there suggests that there is also an 8 byte footer.

Users @Vitali-Kushner and @mark-bessey reported success even with truncated files, so a gzip footer does not seem strictly required.

@tobias-kienzler suggested this function for the bashrc:
zlipd() (printf "\x1f\x8b\x08\x00\x00\x00\x00\x00" |cat - $@ |gzip -dc)

You can just do:

gzip *

gzip will tell you it skips the files that already have a .gz ending.
If that message gets in the way you can use:

gzip -q *

What you tried did not work, because gzip doesn't read the filenames of the files to compress from stdin, for that to work you would have to use:

ls | grep -v gz | xargs gzip

You will exclude files with the pattern gz anywhere in the file name, not just at the end.¹ You also have to take note that parsing the output of ls is dangerous when you have file names with spaces, newlines, etc., are involved.

A more clean solution, not relying on gzip to skip files with a .gz ending is, that also handles non-compressed files in subdirectories:

find .  -type f ! -name "*.gz" -exec gzip {} \;

¹ _{As izkata commented: using .gz alone to improve this, would not work. You would need to use grep -vF .gz or grep -v '\.gz$'. That still leaves the danger of processing ls' output}