Haha, the .tar download itself was a whole other battle for me.
The short answer is the ibdata... and ib_logfile... files are required as well as the steem/ folder, but those files contain data about all the databases on that server. Even so, this approach should work if you backup the entire _data folder, but nothing short of that. That would almost assuredly go faster than dealing with the dump.
Creating my .tar is no walk in the park either. I'm looping through the tables and doing a mysqldump one at a time and appending each of them to the .tar file. This database is so huge a standard mysqldump of the entire thing never finished once in my testing.