It's interesting, I was comparing Liverpool's 84-85 season to their 21-22 season, and they actually played just as many games, 63. In 21-22 they played in 3 cup finals (fa cup, league cup, champions league) and they could have played more games in 84-85 if they didn't go out of the League Cup early.
So overall, there may actually be less games played now than before, at least at the very top. If you're playing in the Europa League, that can potentially increase it by quite a bit compared to how it was in the 80's when it was the UEFA Cup.
Here is what I think is making the biggest difference. Footballers today are pushing the human body to it's limit with training and fitness, I can remember Gascoigne with a bit of beer belly playing for England. Players were eating fry-ups and drinking champagne before games back in those days. Travelling during pre season can't be helping either. Training in different climates and pitches must be difficult. I also think the schedule today is a mess. The Premier League is Friday, Saturday, Sunday and Monday, when it should be just Saturday and Sunday. FA Cup games are on Fridays and Mondays now too.
The biggest problem of all though is the international tournaments. Back in the 80's, the Euro's only had 8 teams, so the tournament was much shorter which meant that most top players around the world were giving their bodies time to recover for the new season. Expanding it to 16 teams was the sweet spot, most tournaments would start June and end before July. It's very different today. We have 24 teams now and each of the last two European Championships has ended no earlier than July 10th. Then there is the World Cup. Scheduling during the World Cup has mostly remained the same, start June and finish mid July, teams have expanded in that time though from 24 in the 80's to 32 today. But it's the next world cup when things are going to get messy, 48 teams with the Final being played on July 19th! This is crazy. You now have two international tournaments finishing way into July. We also have the Nations League replacing friendles, which is yet another competitive tournament, and one that nobody asked for.
There is more to come though. The Club World cup starts in 2025, which means another tournament starting in June and ending in mid July.
The biggest issues are international football, scheduling, current competitions expanding and new competitions forming. By 2025, football will be pushing things way too far.