Liverpool's big win over Bournemouth was very natural because the performance or quality of the Liverpool team was much better than Bournemouth's, so it was not surprising when Liverpool won easily.
Currently, the quality of Liverpool, Manchester City and Arsenal are not much different so it is difficult for us to predict what will happen at the end of the season, but what is certain is that these three teams have the potential to compete fiercely in the race for the Premier League title this season.
I will not underestimate any of these three teams.
It was a really convincing win indeed. In Salah's absence people were wondering what Liverpool were going to do in the games without him. The Bournemouth game was an easy one on paper and Liverpool showed it to us by a solid gameplay. Nunez and Jota scored two goals each to destroy their opponent by 4-0.

I'm quite happy for Nunez to score here. Because he really needed some push to improve his performance. This must have made a good impact on his self-confidence. While Salah is away Nunez has more responsibility to keep the scoring productivity at a good level.
Honestly I was a bit worry about how Liverpool would cope in the league in the absence of their playmaker Salah who was on AFCON duty in Ivory coast even without. Trent Alexander-Arnold, however I was amazed with Liverpool convincing win against Bournemouth in his absence the likes of Nunez, Diogo Jota, Gakpo all performanced brilliantly well without those key players with the win I strongly believe Liverpool would give Man City a run for their money as far the title contenders is concerned, though Arsenal had been very inconsistent so far in the league, however I believe the team would make things difficult for both Liverpool and Man City title bids.
I was thinking the same thing as well, concerning how Liverpool will be able to cope without their hit player, I later realized that one thing with nature is that, nature will always fills every gap, might not be exactly the way you want it, but trust me it will be filled up. You can see that the other players have come to the realization that their hit player is not around, so they need to play to leave up to the expectation of the club and so far they've been doing very well. The players you mentioned in their last match, where very brilliant in their pattern of play especially Diogo Jota and Gakpo.