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It's correct that Windows 7, Windows 8.0 or Windows 8.1 are not supported on 7th generation processors depending on the graphics that the processor has.
Regarding Linux* please check the following link where you can find Supported Operating Systems for Intel® Graphics Products Linux* OS is supported on that and different generations.
Intel does not provide direct downloads and technical support for Linux drivers. The Intel Graphics Linux driver is primarily supported through the original equipment manufacturer (OEM), the Linux distribution vendor, or by the Intel Open Source Technology Center at 01.org/linuxgraphics.
Depending on the processor you have in mind you can visit https://ark.intel.com/ then look for the processor model you want and you can find the integrated graphics model that comes with the processor.
Example: Intel® Core™ i7-7700 Processor ---> processor graphics ---> Intel® HD Graphics 630
Intel Customer Support Technician