Is playing billiards in this manner considered gambling, and is it permissible to take others' billiard balls even if they were not sold?

Firstly: The game of "marbles" (Billi) is forbidden gambling if the winner takes the loser's marbles, because marbles are purchased with money. The ruling of prohibition applies regardless of what the winner does with the marbles afterwards.

Secondly: Wasting five hours a day playing is a deprivation and a squandering of time, about which one will be questioned on the Day of Judgment. Some games, even if free from gambling, may be prohibited if they lead to addiction and excess, due to the corrupting effects they entail and their undermining of one’s dignity, even if the type of game itself is permissible. Some scholars have explicitly stated that if a permissible game takes over a person's concern and occupies their time, it becomes forbidden.