In many old games like Medal of Honor and the old WW2 Call of Duty's, every time you pick up a STEN, the character holds the magazine like a horizontal grip of some sort, however, in more recent games like Battlefield V and Call of Duty WW2, you never see a character doing that, so it got me questioning, why they didn't do the magazine holding thingy, cause it is way cooler than just holding the gun normally...
Strictly according to the manual, if the Sten didn't have a foregrip (the MkI and V did, usually) the soldier was trained to hold the gun by the barrel shroud, as instructed in this manual for the MkII (unfortunately poor quality scan). You'll notice that the instructions specifically state to not hold the gun by the magazine.
However, Sten magazines were notoriously bad - the design was a poor one to begin with, and the early magazines especially were made in a great rush with quite loose tolerances which could lead to feed problems during firing. So in practice it was not uncommon to hold the gun by the magazine housing to be able to brace the magazine and stop it wobbling about so much during firing, and thus potentially reduce the likelihood of a jam. The more skilled user would by all accounts test each magazine before use to make sure the fit was acceptable.