Energy systems require flexibility to help with the penetration of variable renewable energy. A promising solution for flexibility provision is demand-side management (DSM) from industry. However, the extent of flexibility from industrial DSM depends on the characteristics of industrial processes. In this work, we investigate the potential of industrial DSM as a flexibility provider to a net-zero sector-coupled energy system. Specifically, we investigate the cost reductions and the change in deployment of other flexibility options due to industrial DSM. We examine three system configurations for the Swiss sector-coupled energy system, varying the attractiveness of alternative flexibility options. To consider the characteristics of industrial processes, we parameterize the study with three representative industrial process characteristics: load-shifting potential, storage capacity, and losses. Our results show that the value of flexibility from industrial DSM highly depends not only on the process characteristics, but also on the system's flexibility alternatives, particularly for flexibility over longer time horizons. Due to differences in flexibility alternatives, the maximum cost reductions from industrial DSM vary between 2% and 27%. Additionally, we find that the effects of the three investigated characteristics on cost reductions also depend on the interactions with the alternative flexibility options. Depending on the interactions, cost reductions may stagnate as flexibility from industrial DSM is enhanced. Our study shows that while industrial DSM can serve as a flexibility provider to a net-zero sector-coupled energy system, the value of industrial DSM highly depends on both the characteristics of industrial processes and the system's alternative flexibility options. Both aspects must be considered when evaluating the extent of flexibility from industrial DSM.