In addition to the way proposed by Nathan, I would like to add a few further ideas.
One simple way to judge the relative strength of two players is to look at their mutual game history (if it is large enough, of course!) and consider the percentage of won and lost games. For instance the EGF rating system has this property:
This setting gives about 30% probability for beating a 1 grade stronger opponent.
So if one players wins only 30% of the games, we may assume he is one stone weaker. Other percentages can be translated via their formula.
Of course, a large number of games between the two players is required. Also, relative strength is not transitive: It may well be that player A usually beats B, B usually beats C, and yet C beats A more often than not.
Historically, the average score difference in (sufficiently many) even games is a good indicator.
One stone difference in strength equals two komi, and komi is usually around 6-7 points. So, for instance, if one players wins by around 26 points on average, we may assume he is 2 stones stronger.
Obviously, this approach suffers from resignations - the players would need to continue lost games until scoring. simply applying a threshold seems to be impossible in general, and may only be useful in specific instances.
I was interested in seeing how accurately we can judge the level of Go players from their moves and created a website for this purpose: https://kyudan.net
It displays the first 100 moves of an anonymized game. Once you submit your estimation of the respective level of the players, their real rank is displayed. All players are dan level up (so the options rank from 1 dan to 9 dan only). More information about the process are described here.
When I last looked, there were more than 2000 results submitted by more than 100 people. There was a significant (from appearance, I did not really number crunch this) difference in estimation accuracy between different judges. The most accurate people were often within 1 - 2 stones of the real ranks, but on average people were off by 2 - 3 stones. You can see my personal results here.
Considering that simply always selecting "5 dan" will lead to being within 4 stones of the correct answer, it seems apparent that judging player level from a single game is not easy for most of us.