Qualcomm doesn't provide further details on the issue, but we recently heard that Samsung would drop the Snapdragon 810 from its upcoming Galaxy S6 flagship - not because the 810 overheats, but simply because Samsung seemingly wants the new handset to be exclusively powered by its own octa-core, 14nm Exynos 7420 processor. Today's announcement from Qualcomm can probably be seen as a confirmation: the Snapdragon 810 and the Galaxy S6 won't roll together.
Qualcomm's Snapdragon 810 is already being used by LG (in its G Flex 2) and Xiaomi (in its Mi Note Pro). Other big smartphone makers will almost surely also rely on the 810 in the near future, though it's unlikely that any of them will order as many chipsets as Samsung would have done for its S6 (which, of course, is expected to reach millions of units sold in no time).
The good news, if we may put it this way, is that many Samsung fans don't seem to care about the fact that the S6 won't use Qualcomm's processor.