The heck does “upstream” mean in this context? Do they just mean “kernel compiled by someone else than you”, ie. how Linux distros generally work?

No. “Upstream” in the context of Linux generally means the releases you get from kernel.org; Linus’ Linux, aka “mainline”. Hardware that is supported upstream can usually (barring regressions) use the latest Linux releases without needing to wait for someone to port some patches to it (as users of non-upstream-supported hardware must do).

Fully based on the official kernel source code, not tweaked by distributors