Im pretty sure the HD4600 can handle World of Warcraft. Have you checked the HP website for your model to see if they have an updated video driver for your model specifically, or any other updated drivers?
If HP does not have anything, have you tried the drivers located here Download Intel® Graphics Driver for Windows 7/8.1* [184.108.40.20632] ?
Do you know what version driver you have installed now? You can check in the intel graphics control panel under OPTIONS AND SUPPORT then click at the top drop down menu and click Information Center, it will show you the driver version etc.
Also make sure its not over heating, so keep the vents on the bottom and sides clear. I don't know why they don't make laptops you can actually put on your lap, cause on mine anyway, my legs block the vents. When I game on my laptop I have it on a small table with raised rubber feet under the corners so its up about 1/2"
HP only has one thing for graphics/video and its doesn't work (Your computer doesn't meet the minimum requirements to run this program). I just tried the driver you sent and it said the same message. My version is 10.18.15.4248. I have just tried keeping the vents open but it has done nothing.
That's weird. I wonder if your model is different for some reason. Did your laptop upgrade to Windows 10 by chance? Maybe that's why it says that error. Also I see allot of new drivers from Dec 2015 and Jan 2016 including Bios updates, all or some of these could help with your issues HP Software and Driver Downloads for HP Printers, Laptops, Desktops and More | HP® Customer Support. Mae sure your picking the versions for the correct operating system. They do seem to have a link for them to check for you, what updates you need. Maybe that would help. Now I don't work for intel, Im just a user like yourself trying to help, so do this all at your own risk. Im sure an official intel person will reply soon and help you further.
I did update to Windows 10 so I might see if I can downgrade. For the link that's what I have been using through HP though I'm still getting the same errors as before.
The link I sent you for the drivers here in reply #1 was for Windows 8.1, could be why it said it wouldn't work. The newest Windows 10 version is here: Download Intel® Graphics Driver for Windows® 10 [15.40][4th Gen].
I don't know if I would downgrade as some people have had issues reverting back. I have not upgraded myself yet, so not sure what complications may arise from reverting back to 8.1
In your case that your laptop has Windows® 10, I suggest you to run Windows® 10 update; it will install the latest drivers for your device.
A second option; will be from Hewlett Packard website. Sort by Windows® 10. According to your model number, the pc has Hybrid graphics, it is necessary to install the Intel graphics driver and Nvidia® driver.
After updating the graphics drivers, I suggest you to double check Intel graphic’s recommendation for your game at Best Gaming Settings