Everytime I see "GNU Screen killer", I think it has the same chance of surviving as "iPhone killers" or "iPod killers". It might be better, but being touted as something which will "kill" something established, it's almost always doomed to "fail", that term (also) being warranted or not.
I still see little reason to part from screen after all these years, and despite various offers of "better" options troughout the years. On the other hand, I did ditch my iPhone for an Android-phone. Although it was an Android-phone not labeled as an "iPhone killer".
The "X killer" thing is media reaction though, especially of open source projects, rather than necessarily a goal of the project.
I doubt the people working on tmux have "killing screen" as one of their priorities (or even one of their cares). They wanted something that worked differently, and decided that going from scratch rather than using the screen codebase (either because they didn't like the code, or for licensing reasons, or they though they' be touching so much of the existing code that it would just be cleaner to start from scratch, or some combination of the above) was preferable.
It'll take a lot to replace screen, but given it offers features in its stable branch that screen doesn't have or only has in beta (the horizontal splitting talked about since ~2009 has been in beta since then) and is available standard in OpenBSD and probably optionally in every recent Liunx distribution, I can see tmux taking over some of screen's mindshare. I'm told tmux has noticeably lower memory requirements too, though will only make a difference to users who are working with very small environments like cheap VPSs on over-sold hosts or embedded environments, as screen isn't that much of a monster to start with.
FYI: I'll be sticking with screen (via byobu where available) as I know it, it works and is stable (I've not had it hang/error/crash any time in the last <more-than-a-few> years) and it is very widely available.
I'm not saying the product is bad, only that if it gets recognized or talked about as an "X killer" it will almost always fail deliver the specified "killing", and hence it's a "failure" in that regard. You also risk creating higher expectations than you can reasonably deliver.
So basically, announcing your product as or having people talk about your product as a killer of any sort, is mostly a bad thing, be it a good product or not. You want people to say "it's very good", not "it's an X-killer".
Or at least that is my experience and opinion on "X killer" as a branding-strategy.
His point still holds -- the iPhone was never touted as a "Nokia killer" -- it was touted as a "magical" new experience. And the popular press was quite dismissive at first of Apple's ability to compete in the mobile market.
I still see little reason to part from screen after all these years, and despite various offers of "better" options troughout the years. On the other hand, I did ditch my iPhone for an Android-phone. Although it was an Android-phone not labeled as an "iPhone killer".