There was also an exciting moment when I had to install new video card drivers on the laptop, a process which I couldn’t do because the newest Intel drivers were not signed by Hewlett-Packard. Hewlett-Packard last signed drivers in, uh, 2012. Instead, I needed to unzip the drivers, attempt to manually install them, deal with the fact that Windows 7 insisted that the drivers from 2012 were newer than the drivers from 2013, completely uninstall the drivers from 2012, and then re-manually-install the new drivers.
I hope you don't mean that you expect people running integrated video cards on a laptop are going to have to jump through that many hoops to get your game to run. If someone's running it on a laptop, forcing them to uninstall old drivers and manually install new ones sounds like a task that would fall outside their comfort zone, or at least too much of a hassle to bother with. If you have to rely on the latest drivers (or at least newer than the ones windows can install with minimal effort), then supporting it sounds like a bit of a lost cause.
Perhaps I'm being a bit naive here; maybe there are plenty of users who are savvy enough to put in the same work (or at least find and follow the instructions that someone might have on your forums after release), but are nonetheless stuck on a low-power laptop for other reasons.