Still I expected them to try harder this time, because the technologies to develop a good GPU, are strategically important in other areas too

I think I read somewhere that they’re having problems getting AIB partners for Battlemage. That would be a significant impediment for continuing in the consumer desktop market unless Battlemage can perform better (business-wise) than Alchemist.

They probably will continue investing in GPU even if they give up on Arc, it might just be for the specialized stuff.