MySQL Error: “Table storage engine for `proc` doesn't have this option (ERROR 1031)”
The error you got is often seen when you try to use a table option that is incompatible with the storage engine used by the table you're working on. 

For example, 

CREATE TABLE mytable (...) ROW_FORMAT=FIXED;


This table option was deprecated in MySQL 5.7. It will raise an error if innodb_strict_mode is enabled.

You should always run mysql_upgrade after installing an upgrade of MySQL (it says so in https://dev.mysql.com/doc/refman/5.7/en/upgrading.html). Sometimes a new version introduces a change to system tables, and you should apply those changes after you update the software.

I'm guessing you have not run mysql_upgrade in a while, so the dump produced from your previous installation may have still used system tables in the format of some earlier version of MySQL.

So it wouldn't hurt to run mysql_upgrade before dumping the system tables before you upgrade.