It's "anonymous" if it doesn't publish your name/identifier alongside your content. 4chan is anonymous. When you use it, you are anonymous to the people reading your comments.
Does this app pretend at any point that its operators couldn't identify users if they wanted to? That would be dishonest. But what word do you expect them to use for "your name will not be published" besides "anonymous"?
This is a useless definition of "anonymous". It's anonymous to the extent that you care about 4chan, but not anonymous to the extent that you care about prosecution.
Where on Whisper's site do they say "this site is anonymous, but it is not safe enough to publish anything with legal implications"? I looked.
I think they essentially do, which is part of @moxie's point about can't vs won't. Above the CTO says "I can't tell you who a user is without them posting their actual personal information", which is very misleading to the general public without the addendum: "...unless I try to".
Does this app pretend at any point that its operators couldn't identify users if they wanted to? That would be dishonest. But what word do you expect them to use for "your name will not be published" besides "anonymous"?