You recognised the 10th person as employee and possibly included in your pay roll as well. Therefore you are reaching to 10 employee firm. And therefore the act is applicable.
If the part timer is coming regularly i.e., hours are same for each day, or he is coming few days in a week or so, then he/she is also eligible for gratuity. Please refer to definition of employee under gratuity it is clearly defined that part time employees are also eligible for payment of gratuity. However other stipulations under the act including completion of 5 years of 'continuous service' etc are applicable for 'part time employees' also . You may read more here in this link -
(e) "employee" means any person (other than an apprentice) employed on wages,  [***] in any establishment, factory, mine, oilfield, plantation, port, railway company or shop, to do any skilled, semi-skilled, or unskilled, manual, supervisory, technical or clerical work, whether the terms of such employment are express or implied,  [and whether or not such person is employed in a managerial or administrative capacity, but does not include any such person who holds a post under the Central Government or a State Government and is governed by any other Act or by any rules providing for payment of gratuity].