This is how I understand them. - Watch sb/sth doing sth: implies watching something continuing for a duration, often continuous or repetitive. - Watch sb/sth do sth: implies the action watched is transient and short. However, the distinction is not always clear cut, so the two may be used interchangeably in many cases. Examples: - I watched the car approach and zip by at a hight speed - the action is transient and one time occurrence. - I watched her reading a book in her armchair - the action goes on over a period of time without much change.

I watch her play games everyday, it is simple tense, means some thing happens frequently. I'm watching her play games right now, it's progressive tense, which sth I'm doing right at the moment.