Meaning # 17 in the LDOCE refers to 'letting out' a room or a building. This does not refer to smaller items that a store rents out.
Please have a look at the definition of let out from the link I have listed below let out : to grant the occupancy or use of (land, buildings, rooms, space, etc., or movable property ) for rent or hire (sometimes fol. by out).
To begin with, you were looking at let, not let out. The definition adds that in this use, let can sometimes be followed by out, but it's not the common way to use the verb in the kinds of situations given.
Perhaps more important for this discussion is the fact that they say "movable property." Why did they add "movable"? It's because they're thinking of large things not commonly considered portable, like large pieces of furniture. That's the reason they say "movable property" as opposed to just saying "property," Mido.
One extra point I'd like to throw in here, and I hope it comes out right: If native speakers say that they don't hear or use a phrase, that means people learning the language should accept that the phrase in question either doesn't exist or is used by such a small minority that it isn't something they should use in their pursuit of better English.
In a nutshell, we never say let out a DVD. You can let out a room full of furniture, but not something like a DVD.
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