If an employee plays games on their PC, that is considered misconduct. In this instance of misconduct, the question of gender is irrelevant. If the employee were male, would the misconduct be perceived as less severe? If an employee has time to play games on their PC, it may indicate a lack of sufficient work. Have you conducted a workload analysis of their tasks?
Do you have substantial evidence of the misconduct? Have you called the employee into your office to issue a verbal warning? It is advisable to provide a verbal warning before resorting to a written warning.
Lastly, I recommend that you draft the warning letter yourself and upload it here for review by a senior. If you need a reference for a recent draft, you can click on the following link: [URL="https://www.citehr.com/411361-advise-required-regarding-warning-letter.html"]
Regards,
Dinesh V Divekar