As psuter pointed out there is Evil mode for Vim. There's Viper mode too, which I believe is older. This isn't a new thing. Vim as an editor isn't anything special....infact it kind of sucks. The script/plugin/extension ecosystem is nice but that seems to be in spite of vimscript. Evil mode in Emacs is pretty nice.
Evil mode is one of the better Vim emulation layers for non-Vim editors...and there are quite a few.
Sublime Text has a much better GUI front-end than gvim or MacVim. So for someone who doesn't want to work in a terminal and wants to use a GUI based editor, they may feel that a fully featured vim mode in Sublime Text would offer the best of both worlds: rich keyboard-controlled text editing and a beautiful front-end GUI.
I just use vim inside tmux, but that's mostly because I have to write a significant amount of code on a remote machine via ssh.
Also, I will say that even as a dedicated vim user I wouldn't be thrilled to use vim without a large number of plugins that more or less just offer features something like Sublime Text can offer natively, like a decent file tree browser. So a vim mode in Sublime Text can make the barrier to entry lower by reducing the need for the modern programmer to load up vim with plugins.
The combination of using vim and having to debug stuff in awkward places (on boats in rough seas, 20ft in the air on hydraulic scaffolding, in garages) with text-only interfaces (serial terminals), has totally changed me. I went from having 4 monitors to working on a 13" rMBP.
My personal preference is vim in a quake-style terminal (yakuake on linux or iTerm2's hotkey window in OS X) with a minimal amount of transparency so that I can "read through" the terminal and see whatever's in the browser/document window behind. After getting this set up, it's going to take a lot for me to switch back to an IDE full time.
And yeah - gotta love screen/tmux.
I personally try to use a minimal number of plugins. Command-t is the only one I use daily. I gave eclim a shot for java stuff, but ultimately found I didn't use it very often. It's better to just not fight "the vim way," though I definitely see how that's a barrier.
I still love using multiple monitors (I currently dedicate an entire 27" monitor to a single full-screen terminal with tmux as the "window manager"), but it is really nice having the know-how to do the full development cycle from a terminal. I used to be afraid of command-line stuff and I think it really held me back in some ways. Because I used the terminal only when forced to I never could remember how to actually use it beyond the most trivial stuff, which just made it more frustrating when I had to. And I never could find a true tiling window manager on OS X that I liked; tmux works great for that out of the box. I still want to experiment with an xmonad-based workflow on Linux, but I haven't really had a reason to yet.
My job forced me to get over that, and though I can still appreciate a good GUI-based editor I don't feel any need to switch to one anymore.
...which is something people have done [1]. The goal of these extensions is usually to have the best of both worlds. E.g. block selections in an editor you can script with elisp.
Vim's modes are quite powerful and easy to get used to.
To some extent it is probably people not learning their new editor completely and another part is sometimes the vim-way is just easier/quicker.
Being able to escape insert mode and start modifying the text is great to a vim user things like editing inside quotes `ci"` are easy to do without a mouse, as is moving around the file without leaving home row.
I am a dedicated Vim user, but I would assume people looking for an IDE instead of an editor, with tab-complete, file browsing etc but don't want to install and configure the myriad plugins required to get Vim into this state; would prefer Sublime.
Wouldn't this be a bit like building a 'vim mode' for emacs?