The problem, as I see it, with that definition is that you have a range in these games from 0 choices to a "gazillion" (or whatever- an extremely large amount in some cases). And you are drawing your distinction between (say) 8 and 27 choices. For me, a Visual novel is a pre-written linear story- there might be an early choice or two in what character story (out of several) you want to follow, but the basic path is predetermined.
"Chose Your Own Adventure" (Is that a trademarked term?) is probably a more accurate term for these kind of games. That sort give you more choices, but it's still a limited range.
I wasn't aware of "Sandbox" being used in that way- I've always heard of it used as a testbed system. ("Let's go play in the sandbox.")