Several games will check to see if your PC/laptop meets its graphics hardware feature requirements before they'll try starting or running. Sometimes what it checks for, & sometimes what's missing isn't related to how powerful that graphics hardware is, but rather they can be features that were just never added to your hardware's driver set. One solution can be to run the game in a VirtualBox Virtual Machine [or VM], which particularly for casual &/or on-line games can have additional benefits too. Not every game will work in a VM, but quite a few will.
A VM is a fake PC -- software pretending it's hardware -- and software including Windows can't usually tell the difference. A VM's fake graphics hardware may include features your real hardware doesn't. You control how much CPU & RAM the VM can access, so you're not wasting loads of power on a game that requires fairly little -- many of these games will use the same percentage of your CPU [& sometimes GPU] regardless how powerful either of those are. If you have a 4 core CPU, you can for example donate 1 or 2 to the VM, & keep working on something else in the background, or foreground if you wish. You can also change the resolution or screen size easily, or in effect run any game in a resizable, minimizable Window -- you control the VM's window, even though the game inside is running full screen.
VirtualBox is VM hosting software -- the software that pretends it's a PC. It takes up about 180 MB on your HDD, plus it adds several drivers.
https://www.virtualbox.org/
There's also a portable launcher.
http://www.howtogeek.com/188142/use-portable-virtualbox-to-take-virtual-machines-with-you-everywhere/
http://www.vbox.me/
Setting up a VM means installing V/Box or setting up the portable launcher, then creating a VM, which is the part you'll actually use. Generally speaking setting up a VM is pretty easy -- select the OS, accept the defaults, & then install a copy of Windows to that new VM's virtual hard drive. A Virtual Hard Drive [VHD] is a single file that pretends to be a regular hard drive. With little software added it'll probably be between 15 & 20 GB for a win7 install. Once you create a VM, you can copy that single file wherever you want, so you can store a copy, do whatever you want to the VM, & restore it with a simple copy/paste. You can keep different versions too, & you can add VHDs to a VM, same as adding a hard drive to your PC. You can for example create a VHD, mount it in Windows so it's like a regular drive, &/or use it with one or several VBox VMs -- and you can use it for something like storing most of your games. In that last scenario you could mount the VHD like a regular drive in Windows, or unattach it & have access to everything on that VHD from your running VM -- accessing a regular drive from a VM isn't nearly as simple, involving networking & sharing. A final benefit, you don't have to worry about backup software or copying/cloning that drive, since it's just a single file you can copy wherever you want, as often as you want.
Now, the sticky part... Windows in a VM needs activated the same way as the copy of Windows that's installed on your PC/laptop. One way to do it is to buy another license, or use an old one -- another is to use win7 in a trial install [Google for all sorts of info, details etc. on stuff like extending the trial period that might cause a frown or two if posted here].