Digital games represent one of the most compelling fields in computer science, embodying a wide variety of technical challenges. Thanks to the evolution of streaming and broadband technology, new service provisioning schemes have emerged. Remote play streaming services represent an interesting case study deserving a thorough investigation. To this end, we present a network measurement study that can be useful to create traffic models and help researchers identify issues, guiding architecture and protocol design. Moving beyond latency and jitter issues, our purpose is to understand whether remote play streaming services can operate through regular connectivity or, on the contrary, are doomed to fail as happened to some pioneer providers. We have hence deployed a testbed to test the impact of network limitations and, different from previous studies, we particularly emphasize the role of the available bandwidth in this context.