Budget gaming on Intel? That was a good one. Intel won't sell this chip cheap. The problem is, it will be hard to justify premium prices if you can offer only 4 cores. And no, that core comparison was plain dumb. The 4700 has half the cores but the same number of threads. So, unless we don't know utilization of all cores or actual power consumption this says us nothing. AMD's Ryzen 3300X achieves a similar score and has 4C/8T, just like the 1165G7. And I think it wouldn't have been a problem to put it in a 25/35W package if optimized for mobile devices.
Finally Tiger Lake seems to be a step forward for Intel. But I don't see it any better than the older AMD Renoir. Single core performance might be 20% higher or so due to higher clocks and higher IPC. But multicore performance will be way slower at probably still higher power consumption. That small iGPU advantage in synthetic benchmark will likely not translate to real world performance or even turns into a small disadvantage in real games. And don't forget, next year AMD will launch RDNA 2 based mobile chips. Those will offer a completely different level of graphics performance. Even a 12 CU Vega based SoC would kill Xe and that would be easy for AMD to implement. Zen 3 will also significantly increase performance. So, Tiger Lake looks like damage limitation, not more.