No credentials are required to access the tinyurl api. It is dead simple, requiring only the long url in the query:
http://tinyurl.com/api-create.php?url=<longUrl>
A spreadsheet function similar to those in the referenced article would be:
= importData(concatenate("http://tinyurl.com/api-create.php?url=",B1))
Reference: Tinyurl has an API.