You can do this with a simple regex, using the =~ operator inside a [[...]] test:
if [[ $file =~ \.gz$ ]];
This won’t give you the right answer if the extension is .tgz, if you care about that. But it’s easy to fix:
if [[ $file =~ \.t?gz$ ]];
The absence of quotes around the regex is necessary and important. You could quote $file but there is no point.
It would probably be better to use the file utility:
$ file --mime-type something.gz
something.gz: application/x-gzip
Something like:
if file --mime-type "$file" | grep -q gzip$; then
echo "$file is gzipped"
else
echo "$file is not gzipped"
fi