I did follow your link to the Oxford English Learner's Dictionary, and I did note that the sentence that looks an interesting book; however, that is a very odd usage that, to my American ear, sounds incorrect.
Look is being used as an linking verb in that sentence meaning to appear or to seem. When used that way, look is an intransitive verb and therefore should not take an object.
Ordinarily a preposition such as like or an infinitive such as to be follows linking verbs such as seems, appears, looks, etc.
It should be more like these examples:
That looks like an interesting book.
That appears to be an interesting book.
If you want to omit the preposition like, you would need to change the syntax. With a linking verb, you can use an adjective in the predicate. Note the following example:
That book looks interesting.
Interesting is still modifying book. It does not need to precede the noun when a linking verb is used. This is called a predicate adjective.
The only other way that I could write that in the same way would be to use the verb to be, but that would change the meaning. Take this for example:
That *is* an interesting book.
That is grammatically correct, but it significantly changes the meaning of the sentence though