A better term would be "timbral recognition" but for some annoying reason, the guitarist community tends to use 'tone' to mean 'timbre'.
Incidentally I don't
think the Line 6 device actually does what the original poster believes it does. Rather than automatically try and match something it's hearing, you provide it with a song title and it searches an online presets database full of user-submitted patches. It certainly doesn't synthesise any new patches based on what it's hearing.
It's an interesting approach, but works well for guitarists because emulating another guitarist's sound is not all that difficult given a multi-fx modeller like the Line 6 series, and because that's a common pastime among guitarists. I'm not sure that it's quite so easy to emulate synth sounds given that synths differ quite a lot and they are generally more complex to set up.
What would be great is if VSTis had a much more comprehensive way of classifying patches. The Native Instruments ones tend to have a really good patch selection system that lets you filter them on various criteria, but for some reason the majority of synths still just like to present you with a massive list of presets and leave you to it.