Got back to this today. thanks for your help Andy. Thinking about versions got me moving in the right direction so I didn't need to install an older version and then update.
The problem was very simple. The old version of LinksSQL used the table prefix "links_" the new version uses the prefix "lsql_" That is why I could see the data in MySQLMan but the program wouldn't import it.

MYSQLMan also showed me the old tables with the prefix "links_" and the new tables with the prefix "lsql_" that it created when trying to read the data. After I figured out what was going on, it took exactly two minutes to install the backup data.
I can share some other tips, to help people save A LOT of time as compared to some other solutions posted here, beginning where I needed to begin last week
A lot of threads in this forum talk about importing .def files. The .def files contain all the mods you might have made to the default fields in the links and category tables. So you need those changes in order to successfully import your data. But if you have a backup of your database that was created as a dump, all that information is contained in the data file.
1. Use mysql commands from the shell to restore your backup into the database.
2. Go to Admin: Setup:SQL Server: Fill in all the database info (server, name, password, etc). The default prefix will already be shown here. IN my case it was "lsql_" But if you are uploading data from an older version, open your backup file with MySQLMan or with a text editor to see what the prefix really is. In my case it was "links_" SO I changed "lsql_" to "links_" and everything worked fine.
3. On the same screen, select "Load data from an existing set of tables(or resync the def files if you have changed them manually" and submit. Now all the defs are automatically updated.
4. Next, if you're importing data from an older version, you need to account for the fact that the new version of LSQL may have new data structures. So you have to go back to Admin: Setup:SQL Server: and select "
Create new default Links SQL tables in this database but do not overwrite any existing data." This will add in any tables that were not in your older version (like payments and reviews in my case). I think this step will save a lot of people from having to manually edit there data like i read about in some threads. 5. Next you go to Database: click repair tables
6. Go to Database: click rebuild search
7. Go to Database: select categories and properties from the popup menu, click GO
8. Now go to the bottom of the screen and click "resync database", do the same to resync "links", "users", and "reviews"
Presto Chango! Now your database is completely updated. click dynamic to display your directory and you can see if everything is working OK.
If everything is OK, you should back your data up again now in the current LSQL format, so next time you can restore without going through all these steps.
I hope that is helpful, let me know if there is anything wrong here.