Here's some Unigine Heaven benchmarks I found on YouTube for the new 16" MBPs, alongside my iMac 5K with Vega 48 and another iMac 5K with 580X. As you can see, both the 5300M and 5500M are slightly faster than the iMac 5K with Pro 580X for gaming, but not as fast as the Vega 48. Note, I haven't found benchmarks of the 8 GB 5500M, but with such an old benchmark, I think it will be about the same as the 4 GB 5500M here.
Unigine Heaven (OpenGL, Ultra quality, Extreme tessellation, 1600x900 8xAA) / Extreme Preset
2019 iMac 5K, i9 9900K, Pro Vega 48 - 71.3 fps (33% faster than MBP 16" with 5500M)
2019 MBP 16", i9 9880H, Pro 5500M 4 GB - 53.3 fps
2019 MBP 16", i7 9750H, Pro 5300M 4 GB - 47.7 fps
2019 iMac 5K, i9 9900K, Pro 580X - 45.6 fps (14% slower than MBP 16" with 5500M)
Interestingly enough, the 5300M is VERY close to the performance of the 5500M and still beats the Pro 580X. However, if you actually plan to game on you're computer, I would recommend getting the 8 GB 5500M. A couple modern titles like RDR2 need more than 4 GB if you want to turn texture quality all the way up.
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Expect about half the performance based on geekbench 5 scores.
My 2017 imac with the 580
34579 Metal
2019 16' MMB - Base 5300m
21,328 Metal
If you upgrade to the 5500 that'll help a bit but it's unlikely that the 16" can sustain that during a prolonged gaming session without having to throttle down from the heat.
Even if it does, this is still not close to the 2017 imac and even THAT isn't a game machine, it's only about in line with the ps4 pro for real world gaming experience. Expect ps4 levels of graphic ability on this laptop
That's not a good representation for gaming though. That benchmark measures compute performance, which can be quite different. The new AMD 5000 series cards are more optimized for gaming, whereas AMD was more focused on compute performance with the old 400/500 and Vega series. As you can see in my Unigine Heaven benchmarks above, the 5300M and 5500M actually beat out the 580 in that gaming focused benchmark.