A simple bash one-liner!

gunzip -c /path/to/backup/mysqldump.sql.gz | grep -E "^CREATE DATABASE" | wc -l

Breaking this down..

This prints the contents of a gzip compressed mysqldump to the terminal

gunzip -c /path/to/backup/mysqldump.sql.gz

Grep for lines that start with CREATE DATABASES…

grep -E "^CREATE DATABASE"

Count the number of create database lines..

wc -l

So to count the number of tables it’s just a simple change to…

gunzip -c /path/to/backup/mysqldump.sql.gz | grep -E "^CREATE TABLE" | wc -l