Mini-pci-express slots are usually running at X1 or at most x2 speeds and as such are limited by bus bandwidth.
Laptop processors are usually far weaker than desktop equivalent versions.
If this was desktop, then yes 1050TI would be a big improvement over current 820 laptop has but... Since it's laptop, less powerful cpu and limiting bus speeds, while it will no doubt be faster than the original, CPU will still bottleneck stuff, especially if games are CPU intensive.
So.. yes, 1050Ti will beat pants off 820G that the laptop has but.. CPU/pci-express will bottleneck things.
Avoid CPU intensive games and it might be worth it.