Non-negative means positive or zero. Presumably, gamma could be zero.
Options have positive gamma. If you’re long an option then you’re long (positive) gamma, so your portfolio has positive gamma. If you’re short an option then you’re short (positive) gamma, so your portfolio has negative gamma.
Brooks is correct.
Chen’s wording is poor, which is what makes his statement incorrect. The options have positive gamma, and it’s not the options that are long or short, it’s the position in options that is long or short.