This is just the way it's done with Sublime.
This is the quickest keyboardy way I know of (on Windows):
Ctrl+k, Ctrl+SPACE (Set Mark)
Ctrl-f some word, ESC, Cursor left (Move to start of search string)
Ctrl+k, Ctrl+w (Delete between cursor and Mark)
And then if you're being thorough:
Ctrl+k, Ctrl+g (Clear Mark)
I agree that on Vi/Vim it's quicker, but I think that's just because it's a modal editor, and that particular action is well-suited to the structure of Vi commands.
Linguistically speaking, a non-modal editor like Sublime has a different word order, and the verb doesn't appear until the end, so you usually need some way of defining your selection first and then performing a command.
You may also like to think of this as something like Reverse Polish Notation: you have to set your start- and end-position parameters before applying the delete operation.
It would be the same on pretty any editor that doesn't have Vim's endearing quirks.
(Disclaimer: I've been editing with Vi and Vim for about twenty years, on nearly every system I use, so I know it and depend on it - it's my editor of choice. Sublime is the first non-modal editor I've found which I enjoy using as much.)
I'm sure there's some set of operations which are much quicker in Sublime than in Vim, but at the moment I'm finding it difficult to think of any, apart from Paste and Indent and Toggle Comment.