No, the equivalent would be a kernel panic that the other user had linked. This is a situation where the RAM is fully used and a program's request for memory cannot be fulfilled. This is still a very bad situation because pretty much everything will grind to a halt. The Linux kernel thus makes a decision to kill a process (or multiple) until enough RAM is available again. Usually it kills the process with the most used RAM, but there's methods to influence the decision.
Nope, this is "Your system ran out of memory and now this program isn't reacting anymore (it's trying to allocate memory but there is no free memory left). Please stop the program or try to get rid of some of its subprocesses to free up memory."
Not yet. It can lead to that point, but this is just the kernel handling an "out of memory" situation. The kernel in the screenshot is configured to run its OOM reaper / OOM killer.
The OOM reaper checks all running processes and looks for the one that causes the least disruption when killed. It does that by calculating a score which is based on the amount of memory a process uses, how recently it was launched and so on. Ideally, a Linux desktop user would simply see their video game, browser or media player close.
This smart TV is in real trouble, though, it probably already killed its OSD, still didn't even have enough memory to spawn a login shell and is now making short work of strange VLC instances that probably got left behind by a poorly written app store app :)