why there's no Win10 choice for drivers in HP support website?

Seems to be telling you that no driver exists for Windows 10 OS.  You might try the Win 8 driver just to see if it works for you, but at the moment, a Win 10 specific driver is not available from them.

You did not give us the model number of the device you are wanting to update.  HP never created any Windows 10 drivers for many devices that were released before Windows 10 was created.  they do not have the resources to go back and create drivers for all the hundreds of old devices the released in the past.  

Usually the device will function without any drivers.  Windows 10 has generic drivers which work well with most of the hardware released in the last 5  years.  If you have problems with a hardware device, you can also try the Windows 8 drivers.  Most of them work with Windows 10, and in many cases they are actually the same driver.  The hardware has not somehow changed between Win 8 and Win 10,  It is still the same piece of hardware and has to get the same commandment and information, so the driver that worked with 8 usually works with 10.  

your computer is too old, and its parts have no drivers.

if you want Win10, you need something made this decade.