I don't understand how 多くの方向 (that I think means "many directions") means the same thing that 向かう方向(that I think means "direction to follow")?
First of all, in modern Japanese, 途方 is almost always used in set phrases (途方もない and 途方に暮れる), and it never refers to a physical direction. 太平記 was written in the 14th century. Many other monolingual dictionaries of modern Japanese do not even mention this usage related to physical directions. So I guess the author of goo辞書 thought these old definitions of 途方 (多くの方向 and 向かう方向) are so trivial that they can be crammed into one item.
(By the way, this page about 太平記 translates this part as 途方にくれている...)
I guess 多く means more likely second definition in this case.
Given the second definition, 多くの方向 means an approximate direction.