Sorry to get technical, but most classical music pieces aren't "songs." A song is a specific kind of musical form - usually (though not always) a short piece of music with (usually, but not always) people singing. Some classical composers did write "songs" (such as Schubert's song cycle) but most classical music pieces are other forms such as sonatas, concertos, and a long list of other forms.
Don't worry, you're not the first one here to do that, I just had to get it off my chest here.
Anyway, on to your question: This is another one of those "it could be anything" pieces. Heck, it might even be some obscure artist's "song" -- if that 3+ minute segment is all there is of it. As others noted it does sound a bit like Satie ... but it also sounds like a lot of other potential composers (sounds also a bit like Ravel or Debussy). It could be something obscure by a little-known composer, or even a self-written piece by the person who made the video.
If it is something obscure, you may never find out who and what it is. If you like that kind of "sound" a lot of us here can help you out with similar pieces, even if we don't know who did that specific piece in the video.