It will really depends on what he plays; looking above the full upgrade solution would be good, but more expensive and as you say he cannot really afford that. Swapping your 7700K in for his 6500, that IS probably worth it to him as an interim step if his system will accept the chip.
As already stated, you are going from 4 threads at 3.2-3.6GHz, up to 8 threads running 4.2-4.5GHz, that would be a substantial uplift, a good 20-30% in clock speed alone in some cases, let alone the extra threads. His GPU is going to be the bottleneck in GPU heavy titles; but its not uncapable, its around 1080 level, and the CPU will have a beneficial impact on his loading times, and also his minimum framerates; the additional threads will also be used in a lot of modern titles, giving him more headroom for both maximum framerates, but also to ensure the CPU isn't getting threadbound and bottlenecked, causing stutters and lower minimums; and those have a bigger impact to 'game feel' than your maximum framerate.
A lot of more modern games can use those additional threads to spread load; so I think he would find it would be a better experience, and just that bit nippier and more fluid across the board due to the higher clocks, and increased threading; which in turn would make the system viable for that much longer.
Yes there are games that will suck back more; and higher GPUs demand more CPU resources to keep up, but a 7700K will still play the vast majority of titles well when paired with the right GPU, and the right game configuration/settings.
Long term, a new platform would have course be better, at the same time it'd be considerably more expensive; for £50 after trading in his current CPU, I'd say the 7700k would be a worthwhile upgrade, and then he could look to do an entire platform upgrade in a few years time if he finds it necessary.