Like I said, I see why yourself and others are making the connection. What interests me is what elements of Team Ico's work are we really seeing repeated here, and of those elements, which can really be said to be unique to Team Ico?
People can be quick to claim Rime is a clone or a ripoff, but I'm not sure Team Ico really own the idea of 3D puzzle/exploration games with young male protagonists. There's a difference between having similarities and being a copy.
The boy I'll grant you, but emotive music is nothing new. The environments actually felt quite distinct to me; Team Ico's work tends to have a very solemn feel, with lots of desaturated colours and grimy textures. Rime feels quite different to me, with loads of bright, bold colours and cleaner, more stylised textures. The world also seems to be teeming with life, which is a big change from Ico at least (which I played for the first time very recently).
That's just me, though.