I found this tweet to be an interesting question and one that I thought should take a few more minutes to think and talk about.
My initial thought was that team would be comfortably 4th and maybe be fighting with Chelsea in the table. I also thought to myself there are some historical ratings that go back that far and I wonder how it looks on those.
First is Elo.
On the last day of the season for 2015/16 Arsenal were ranked as the 9th best team in Europe and the second-best team in England (behind Manchester City, Leicester were ranked 13th).
Arsenal had a rating of 1844.
That 1844 ranking would put Arsenal 11th in the current European rankings on par with Barcelona (1844), ahead of Atletico Madrid (1832), and just behind... the current Arsenal (1852).
By this ranking that Arsenal team would still be the 5th highest-rated team.
Looking at average ratings doesn't change things too much, the average over that season was 1831, the max rating for Arsenal was 1864. So even at Arsenal's peak of that season, they are slightly behind the current rating for Manchester United at 1868.
This one we will not be able to look at quite as deep because the historical data isn't quite as deep there and we will have to use the beginning rating of the 16/17 season as a good enough proxy.
Again there is no SPI for that season but the attack rating of 2.3 would be the 4th best in the current Premier League (better than current Arsenal's 2.1). The defensive rating of 0.8 would rank in the 8th to 10th range (worse than current Arsenal's 0.5).
Basically that Arsenal team is not far off current Tottenham and current Manchester United and not rated as highly as the current Arsenal.
I am going to revise my snap judgment in light of this data. The current Premier League is very strong and the 2015-16 season was unusually weak. My gut feeling tried to account for that but probably didn't adjust enough.
That 15/16 team is probably not all that different in overall quality than the current team. I will say that I do think that team had a bit more "elite" players and maybe that would be enough to tilt the scales in their direction but overall it is probably a favorite for 4th rather than a genuine contender for 4th.