Apparently Rebbi Eliezer ben Yakov is only talking about tying a rope across the entrance of the compartment of an animal that is already "trapped," such as one's cow which is in his yard (see Shulchan Aruch 317:6).

The Gemara earlier on 106b indeed says that whenever the animal is in an enclosure but not easily caught, catching it is considering trapping. A cow, though, does not require "catching" if it is in one's yard. If an animal which does not tend to run away when one tries to take hold of it, catching it is not Tzod (Beitzah 24a). It is not similar to closing the door of a house in order to prevent a gazelle from getting out (Mishnah 106b), because a gazelle is an animal that is not considered captured even if it is in one's house, because it can jump around and get out the door and run away.

All the best,

Y. SHAW