Are there codecs or codec packs?
If you use an Android device with Google Play Services, Google has a document which requires what the device MUST have:

Current Android Compatibility Definition Document - 5.3 Video Decoding 

As you have an Android 5.0 device this document would apply:

Android 5.0 CDD - 5.1.3 Video Codecs

Note that your video file is an AVI container format which isn't listed so it would be up to the manufacturer to support that format or any additional codecs.

As to why can't you just add a codec see this StackOverflow post:

Adding video codec to Android

The short version is that codecs are in ROM and you can't write to ROM unless you are creating your own Custom ROM.

TL;DR: No, you can't add codecs. Use a third party player which supports your format or convert your video to a supported format (both of which you've rejected).