sbenrap: On at least one of the laptops, changing the core affinity resolves the stuttering.
Please try choosing CPU0 and CPU2 for the game from the Windows Task Manager affinity menu and let us know if this solves the issue for you as well.
(On Windows 7 -> alt-tab out of the game, right click the taskbar, choose 'Start Task Manager', chose the 'Processes' tab, right click the 'TeslaEffect' Image name, choose 'Set Affinity', leave only CPU0 and CPU2 checked)
I chose "Set Affinity" and it said "The operation could not be completed. Access is denied".