Yes they're currently trailing Liverpool, but that doesn't mean they're doomed, as there are still 35 games remaining. What's clear is that Arsenal must be much better than last season. They must be consistent and avoid losing their rhythm midway through the season as they have done previously. Likewise Gyokeres must perform consistently as he is the spearhead and key to Arsenal title hopes.
It’s too early in the league to hope to make anything of the teams at the moment, nothing is set until we’ve successfully seen at least 10 game weeks then, we could know who are the contenders and those that would be battling to take stands on the top 10 on the league table. Arsenal’s lose to Liverpool though, didn’t tell well of the team, those are the sort of games where you just have to take a point and be good but, they lost all 3 points to Liverpool, it would be interesting to watch and injury free fixture of them both.
You are right, it's still early to conclude about any teams performance but from what is already playing out it seems arsenal are not going to be at their best this season or perhaps they might not be able to keep up with Liverpool and Chelsea. Chelseas performance has already been anticipated before the new season started. They made a lot of improvements during the break and they might be a threat to all the teams especially Liverpool
You cannot use only three matches to judge how the performance of a team will be like in the long run. Arsenal was able to win two out of three of their matches and in these three games, they played with two big clubs. Chelsea have only been playing with mediocre teams since the beginning of this season which makes me feel that we shouldn't use the matches played to determine the outcome of these clubs.
The EPL is different from other leagues where even before the season starts, we can predict who will be champions at the end of the season, but in the EPL, it's not that easy. The EPL is a highly competitive league and it can even surprise us when big teams lose to weaker teams. So it's not always easy to beat weaker teams, and this often happens in the EPL.
If you say that Liverpool after beating Arsenal will be difficult for any team to beat, you're wrong. In big matches they sometimes play very well but when playing against weaker teams they make mistakes and lose points. After all it's still early in the season, and the journey to winning trophies is long, and every team has its ups and downs. So even though Arsenal dropped points last week it could be Liverpool dropping points next week as could Chelsea. This is why the EPL is always exciting every season.