Github is not "in love" with this behavior, but I have an entire framework that runs on the same paradigm. I do, however, use the zip. You can hit the raw content following this pattern:
https://raw.githubusercontent.com/YOURHANDLE/THE_REPO/THE_BRANCH/FILE/PATH/ETC
Look for the "raw" option on a particular file when browsing.
Here is a config file from one of my repo in a format similar to how you wish:
https://raw.githubusercontent.com/datamafia/ShopifyETL/master/config.cfg
should currently return
[all]
SHOPIFY_KEY=YOUR-SHOPIFY-API-KEY
SHOPIFY_PASSWORD=YOUR-SHOPIFY-API-PW
SHOPIFY_STORE=YOUR-SHOPIFY-STORE-DOES-NOT-EXIST
SHOPIFY_BASE_URL=SHOPIFY_STORE.myshopify.com-or-custom-FQDN
Pay attention to document type and encoding, these could trip you up. Your JSON may not be JSON via the header (should not be).
One final problem, beyond encoding, is that of private accounts. Once private a big can of work will be put on your plate to auth in and see the data.
The header, mildly changed:
Date: Thu, 13 Apr 2017 00:02:48 GMT
Via: 1.1 varnish
Cache-Control: max-age=300
Etag: "154ec087bc75e501a18e72d4e14a6f17bc2f706b"
Connection: keep-alive
X-Served-By: cache-dfw1840-DFW
X-Cache: HIT
x-cache-hits: 1
X-Timer: S1492012345.3876515,VS0,VE0
Vary: Authorization,Accept-Encoding
Access-Control-Allow-Origin: *
X-Fastly-Request-ID: XYZABCXYZABCXYZABCXYZABCXYZABC
Expires: Thu, 13 Apr 2017 00:07:48 GMT
Source-Age: 35
Document type is "plain" (text), so some casting and checking will be important. There are tools in PHP to handle the incoming data and use as JSON. Good luck.