The talk was under 5 mins so I listened to it throughout - but I still couldn't work out what that pair were trying to say.
Google's dictionary defines texture as "the feel, appearance, or consistency of a surface or substance," which applies to any constructed art as much as to any other "surface". I couldn't see how their string of analogies related particularly to music.
I tend to take a technical view of texture in music as being the relative thickness of a sound (or sequence of) in terms of harmonic density, spread of the 'tessitura' for want of a better word - span, maybe; timbre and dynamic. But it also includes melodic and rhythmic elements - in other words the sum total of sounds at a particular point.
This is just my view but I don't think that texture in music (edit: of itself) has anything to do with emotion or sensuality which is the province of the evolving harmonic progression (including melodic or motivic component). Fine, sensuality is well served by music but texture alone has little to do with it. Equivalent textures could produce the whole range of emotion / sensual reaction. And of course, how we perceive the sounds is so very individual. There are those who are excited to excess by the Rite of Spring or Sensemaya, while others find them unpalatable and provoke annoyance, even anger.
It's so personal a thing.