I ran your code on my WinXP laptop and it works just fine.

I suspect that you need to install: Crypt-SSLeay.

Update: I didn't do anything special. This is an Active State std distribution with Crypt-SSLeay installed by me manually.

>perl -v

This is perl 5, version 20, subversion 2 (v5.20.2) built for MSWin32-x
+86-multi-thread-64int
(with 1 registered patch, see perl -V for more detail)

Copyright 1987-2015, Larry Wall

Binary build 2002 [299195] provided by ActiveState http://www.ActiveSt
+ate.com
Built Jul 20 2015 13:29:53
[download]

Further comment/question:
I commend the OP for posting clear, short code that I was able to run! If the post was lengthy or complicated, I probably wouldn't have bothered. But I could do this easily with some cut-n-paste. I don't get any errors running the OP's code verbatim.

The OP's question was "Why doesn't this work?". My question is "Why does this work?". The only thing I could think of was that I do have this Crypt module installed. I am not sure what is going on "under the covers" that allows my machine to successfully access my $url = "https://www.cryptopia.co.nz/api/GetCurrencies";. My experience with https sites is limited and I profess no expertise whatsoever, but I've never seen an https access fail as long as I have this Crypt module installed.