Kind of implying Bradlee, that size did in fact matter even for Dempsey... But I do not wish to focus on size as an argument for anything as guys here to jump on that p4p thing immediately and nullify that argument.
No. Dempsey was very much an average-sized Heavyweight in his era.


... but at his core he looks nothing like a modern boxer
The modern Heavyweight core is fat, flabby bellies (Wladimir excluded).


From the pic you provided you can see instantly that Dempsey has strong arms and shoulders but at his core he looks nothing like a modern boxer and you can tell that training regimes were way different back then.
Dempsey was one of those fighters who was not a "professional" athlete as we view them today. He worked a hard days work before hitting the gym.
Nonsense.
Fighters today do the same workout as fighters did in the 19-teens, 100 years ago.
In Dempsey's era, Boxing had already been around for a few centuries under different rule sets, but the workouts had already evolved and solidified into the modern boxing workout over a century ago. In the 1880s and earlier, there were Boxing gyms in every major city where fighters and other men and boys looking to learn self-defense would go to train.
Even the order of the exercises is the same:

Boxing Workout
Early morning: Roadwork.
First a stretch, then a run anywhere from 3 to 10 miles mixing in some shadowboxing and sprints.

Afternoon: Gym Workout.
Stretch and warm-up
Shadow Boxing
Sparring
Heavy bag
Speed bag and/or double-end bag
Focus Mitts
Jump rope
Stomach exercises - sit-ups, leg raises, medicine ball.
Calisthenics - pushups, neck bridges, chins, grip work, dips, wall pulleys(thera stretchy bands today), throwing medicine ball, old timers chopped wood whereas nowadays they use a sledgehammer on a tire.

Each part done by rds.
Massage at end.

Maybe some handball in the evening.



^ Very good clip here of some of the Greatest Heavyweight Champs in History.
First half focuses on the very similar training they undertook.

.



Where are the advances and changes that some of you young $#!t-snaps are talking about?

Weights? Not many boxers lift weights.
Lighter weight fighters don't want to add any mass or they'll be over their weight class.
If Heavies add too much mass, it'll impede their endurance.
Dempsey, Louis, Marciano, Schmeling, Johnson, they all were naturally over 200 lbs, but they trained themselves so fine and lean because they needed the speed and the endurance for 15 rds or more.

Two significant differences I see is that boxers nowadays don't include wrestling in their training anymore the way boxers did up until the mid 1940s. And of course, chemicals nowadays. Hell, chemicals are even in the food we eat nowadays. A century ago, food was much more wholesome and healthy without poisonous pesticides, hormones, steroids, and vaccines in the animals, and genetically-modified plant-matter.

Shouldn't there be critical advances by now? Shouldn't there be a better way after over a century of "evolution" in gloved boxing?
After all, it's happened in all the other sports.
Is this timewarp good or bad?

The Boxing Workout remains unquestionably the same after 100 years; there is no difference in the training regime.