I like the idea and I have never heard of something like this before. I listen to music a lot and often find myself hearing a phrase and continue singing it out loud because it's part of the lyrics. It would be cool if I could do that while messaging. But, at the first glance, the app you described is very limiting.
Listening to the whole song could be tiring. We don't always have the time nor are willing to spend 3-5 mins just to hear our favorite part. It doesn't mean we don't like the song.
Messaging the whole song could be a problem due to intellectual rights. The app should have permission to play all the songs available (which could be expensive).
Messaging whole songs could be storage-consuming (one 20-song conversation would take approx. 80 Mb; a few days of these chats and we are close to Gb).
I checked the market and the link you provided. The article mentions the 2014 La-la app which solved the above-mentioned limitations by sending links, not songs, and by an option to send snippets instead of the whole songs. They obviously solved the problem with intellectualright, since they had a "selection of licensed music by popular artists and the option for users to create their own messages by searching YouTube for music and clipping out a section for sending." I would like to see why they didn't suceed.
Just year before, in 2013, the article highlighted the important role of music in future messaging. They also mentioned a Stereotypes app, that allowed forming a group, sharing and commenting on songs, and the PingTune, which tried to make it more simple and straight-forward (was acquired by Eros and implemented in Eros)Now. At that time Tango (WhatsApp competitor) tried to do the same by implementing 30-sec Spotify-connected songs in their messaging platform. They had a fun feature which allows you to click on the song snippet and listen to the whole song on Spotify (solves all of the above-mentioned problems).
In 2015, Msty came on scene with an Apple Music partnership, but also didn't survive (as I was able to track).
A bit newer (2017) app called Beatshare wanted to resemble the messaging and listening to music in a form of a short 10-second song clips. They even added a feature of adding text, picture or a video to a song (like Instagram stories) to make it more interesting. In the same year, Spotify noticed the market gap and launched an iMessage app which allowed a user to send songs using iMessages directly .
Messaging songs has become a standard thing. Apps like TikTok and Instagram allow you to send videos enriched with songs, texts and effects, which users find really cool and more content-rich than just plain text (or a song). There is no word that it's not a big market opportunity, but due to a huge competition, I think you need something more innovative here.
From a brief market overview and user profiles, I would go towards the "deeper" analysis of the songs, emotional characterization and stitching to the emojis. Another idea could be the text-to-speech add-on function that allows you to write a piece of text (2-5 words) and then search for matching song lyrics. That way, when a user receives a message, it gets notified that there is a song implemented into text. When it listens to a message, user can hear regular text-to-speech voice with few words or a phrase sang by the chosen singer. It could sound cool and help users express emotions better.