• Unigram (Windows 10) supports these Blobs fully (you can even replace the font in %LocalAppdata%\Packages\<something_with_Unigram>\LocalState\emoji)
• Telegram X (Android) uses these Blobs for Emoji 5.0-12.0, for Emoji <5.0 it uses the original Blobs, for Emoji 12.1-13.? Noto emoji
• Tusky (Android) uses these Blobs in the EmojiCompat configuration
• If you know/develop another app where you can use this emoji set, please let me know, e.g. in the discussions

Note: I have no idea whether any of these solutions still work, I haven't used unlocked/rooted Android devices for quite some time and currently I'm also more using Windows 10 instead of Linux...

As of now (Android Q), changing a system font requires either root, a custom recovery or a device with support for custom fonts (like Samsung devices for example, although I'm not too sure about emoji fonts).

If you got a rooted device, the easiest method would be to use Magisk by installing this. (Please note that this is some third party stuff. I don't have experiences with neither Magisk nor this module)

(2021-07-16: Updated to refer to the fork by @DavidBerdik)

If you don't use Magisk (like myself) or if you only have a a Custom Recovery like TWRP which lets you alter files in the /system directories, you can exchange the font manually.

0. Download NotoColorEmoji.ttf somewhere on your device where you can access it later
1. Mount /system as read-write (aka make sure you can copy files to it)
2. Copy the font into the /system/fonts directory. But please be aware that this overwrites the orginal file
3. Reboot your device.
4. Be happy!

This method is not system-wide and you can only use it if you are either the developer of an app or if you are able to modify the source code accordingly, but there's a guide on how to use this font in conjunction with the EmojiCompat library.

I don't own such a device. I recommend Googling your device's name and change emoji font or something like this 🤷‍♀️.
Well, I do have a Xiaomi phone now, which has theming support, but I think without a special license which would involve uploading my ID, etc. you can't create/use your own themes. So if someone has such an account and can try creating one based on this font (if that's even possible), feel free to create a discussion or something!

1. Download the font (Arch users: noto-fonts-emoji-blob)
2. Follow a short installation guide.
3. Replace all the references of Noto Color Emoji by Blobmoji.
4. Restart any emoji-using apps and enjoy!

There's a Windows-compatible version of the font available (although it doesn't look quite well).