Initialization Error after restoring a Wordpress site from backup
As you can probably tell, CiviCRM is looking for a table that doesn't exist (at least where it's looking).  Given your context, there are a few possibilities for why.

CiviCRM creates a bunch of tables that are independent of WordPress and about which WordPress has no knowledge.  They may be in the same database as WordPress, or they may be in a separate database.  The connection to the database is stored in wp-content/plugins/civicrm/civicrm.settings.php.  There, you'll see two lines of database information: "CIVICRM_UF_DSN" for the WordPress database connection, and "CIVICRM_DSN" for the CiviCRM database connection.

So, the possible situations:


You have separate databases, and you have been only backing up the WordPress database.  You'll see this if your database connections in civicrm.settings.php differ from each other.  The good news is that if this is the case, you might be able to find the old CiviCRM database sitting around somewhere, and it would probably be unaffected from a bad plugin.
You were only backing up the WordPress tables.  Even if CiviCRM is in the same database as WordPress, if you're using a WordPress tool for backup, it might decide to only handle certain tables.  If this is the case, you may be out of luck unless you still have the pre-restore database around.
You failed to update civicrm.settings.php after restoring the site.  If you had Database A running the site, and you restored the backup to Database B, you'd need to update wp-config.php and wp-content/plugins/civicrm/civicrm.settings.php.  If you neglected to do the latter, and you got rid of your old database, you'd see this.  Likewise, if you simply changed the password on the database user and forgot to update civicrm.settings.php, you'd have this sort of problem.