Okay, that gives me enough information to research. I think you're using libsdl's fbcon. According to your patch there should be debug information being printed into a stderr.txt somewhere.
Looking at the source code, libSDL's fbcon module sets raw mode on the keyboard, which according to
this prevents not just ctrl-alt-f4 but the chvt call itself from operating. Preventing this will probably stop Links from working.
Hunting for SDL_getenv - the usual transport for special-case SDL backend hacks - in fbcon's source shows a few options related to setting resolution and mouse device, but nothing relevant to keyboard. It just grabs it in raw mode - as it should for a graphical program - and that's it.
So, I think this means that Links needs to call SDL_QuitSubSystem(SDL_INIT_EVENTS) before shelling out to an external command, and SDL_InitSubSystem(SDL_INIT_EVENTS) after returning from an external command, to place the keyboard into normal mode and allow chvt to happen when using the fbcon module.