The use of the Octal system
The value might not be in knowing octal itself (although as noted in the comments, there is inherent relevance to it). Rather, it might be what learning different bases teaches about abstraction and the representations of numbers in general.

I think of this Essential Knowledge statement from the AP CS Principles curriculum:


  EK 2.1.1G Numbers can be converted from any base to any other base.


The transition from decimal to binary is one step, and the move to hexadecimal can be an even bigger jump. To then have students see that there can be base-8 or base-32 or base-60 or base-37 is at times mind-blowing. The design of a particular base system, while not entirely arbitrary, is a design choice that comes with advantages and trade-offs. 

Moreover, this process of conversion to and from different base systems strengthens students understanding of the underlying algorithmic process. The example I share with students is that 100 in any base system is equal to the value of that base squared. (Indeed it verges upon tautology.) Part of that is breaking down the idea of the 1s place being followed by the 10s followed by the 100s, etc. and replacing it with 10^0 followed by 10^1, etc. Replacing 10 with 2, 8, 16, or any other integer becomes trivial.

Having students see that 100 is not so much "one hundred" but a combination of base numbers and exponents and why that is is powerful.