Having those two tables as HEAP instead of MYISAM is proper. No idea why you got that error on the BBCODE table without more information. What version of MySQL server are you using? Not PHP client, but Server version.
Actually, I can tell you that it's older than MySQL 5.0.3 which restricted VARCHAR to 255.
Open the create table script with a text editor. Search for BBCODE_MATCH_REGEX varchar(256)
Change 256 to 255. Drop all the tables and run it again.
You'll need to start scratch because when that SQL errored the script died and you did not get all of your tables.
Shame on your host for taking the easy way out.
http://www.google.com/search?ie=UTF-8&oe=UTF-8&sourceid=navclient&gfns=1&q=SQL+Error+%23%3A+1074
3rd link down. took me all of 2 minutes.