If there wasn't any offside on Chilwell's goal maybe things would have been much more different for the Chelsea - Liverpool game. But it was still not seeming easy for Chelsea to win the game of course. They had a quite big dominance in ball possession but when it comes to finding chances there wasn't a big difference.
The problem for Liverpool was that they had big problems on finding the target. Despite 13 goal attempts only 1 of them was on target which ended up with a goal. It looks like Liverpool aren't quite ready for the season as well. But this is only the beginning so let's see the next ones.
I'm honestly surprised to see Chelsea's progress their game is completely different from last season seem more confident although there are still some weaknesses but overall it's fine slowly they will find a more suitable playing style, on the contrary, Liverpool looked a bit different I mean less aggressive as you said 13 shots only 1 on target fortunately that one managed to become a goal but overall Liverpool is not optimal, maybe because it is still the first match.
In another match Brentford drew against Tottenham, as I said before when Brentford conceded 1 goal but after seeing their efforts in attack I guess both teams will draw and yeah the final score is 2-2 not bad for Tottenham who just left Harry Kane.