Is it obligatory to pay a brokerage commission to the real estate office after directly purchasing the house from the owner at a reduced price, considering that the office did not respond after the reduced price offer?

If the situation is as you described—that you reached the house for the first time without the agency's guidance, and the homeowner informed you that he had not listed the house for sale with that agency, and the agency owner did not respond to your request to summon the homeowner for negotiation—then the real estate agency has no right to claim a commission for your purchase of the house.