Causation vs correlation problem in case of fixing other parameters and changing only one
The concept of causality is a little tricky. You can (usually) not test for that. You need to come up with a theory-based idea of how things work, such as if the price for a good goes up, demand goes down. And in empirical applications you need to think about, what other things influence demand, so that you don't omit important aspects of the data generating process. 

When I read your description, it seems that you might have a good chance to isolate the causal effect of the change in difficulty. This seems to be a classical example for "difference-in-difference" (DiD). The only problem may be that you changed the diffculty for all players, so you need to see how to handle this. 

Another thing that comes to my mind is, that you essentially look at survival rates (after X days), this would be a task for "survival analysis.

As a (more or less) naive approach, I would say that your approach goes in the right direction. However, make sure that you control for anything you can, like player characteristics (because it is possible that now different people play your game compared to the past). 

So when you have

$$y = \beta X + \gamma d + u$$, 

where $y$ is D7, $X$ is anything you know about players, and $d$ is difficulty (0 diffcult, 1 less difficult), you should get a more or less good idea, what changing $d=0$ to $d=1$ does to y. When you use OLS (linear regression), the coefficient $\gamma$ should directly give you the change. But remember, this is a more or less naive approach (which should give "okay" results).