As expressed in the comments, the answer to this question depends on how you define 'hunting'. However, using common definitions in biology, hunting is almost used as a synonym to predation (see quoted definitions below). In that sense, the statement in your question is clearly incorrect, since it is describing the the foraging behaviours of predatory reptiles.
The description of reptile hunting in your quote is also too simplistic, and there is a range from sit-and-wait strategies to active pursuit of prey, see e.g. the section Foraging models in Pianka & Vitt (2006).
A couple of useful definitions can be found below.
From Encyclopaedia Britannica:
Predation, in animal behaviour, the pursuit, capture, and killing of animals for food. Predatory animals may be solitary hunters, like the leopard, or they may be group hunters, like wolves.
The senses of predators are adapted in a variety of ways to facilitate hunting behaviour.
predation (prɪˈdeɪʃən) n
1. (Zoology) a relationship between two species of animal in a community, in which one (the predator) hunts, kills, and eats the other (the prey)
predation is a biological interaction where a predator (an organism that is hunting) feeds on its prey (the organism that is attacked). Predators may or may not kill their prey prior to feeding on them, but the act of predation often results in the death of its prey and the eventual absorption of the prey's tissue through consumption.
Even if 'hunt' is often defined in terms of active pursuit, it can also include broader and more passive elements, for instance "seek out; search for", see www.thefreedictionary.com:hunt:
v. hunt·ed, hunt·ing, hunts
1. To pursue (game) for food or sport.
2. To search through (an area) for prey: hunted the ridges.
3. To make use of (hounds, for example) in pursuing game.
4. To pursue intensively so as to capture or kill: hunted down the escaped convict.
5. To seek out; search for.
6. To drive out forcibly, especially by harassing; chase away: hunted the newcomers out of town.
I can see the point by @AliceD that 'hunting' is often (in every-day language) used in reference to "active foraging". However, in my eyes this is too restrictive. Also note that the main use of 'hunting' is in reference to hunting by humans, and some of these hunting methods mimic the sit-and-wait strategies of reptiles (see e.g. some methods for big game hunting and the use of traps). If sit-and-wait strategies are not considered hunting, then you are also excluding some human hunting practices from 'hunting'.