I found a study from 2015 that seems to go into a lot of various aspects of chess and how it affects us physically.
"Biochemistry and Psychology of Chess and Classical Physical Exercise:Concurring or Conflicting Evidence?"
I am going to block-quote their "Abstract", which gives an overview, but you might want to read the full paper, which is only 10 pages long. It is fairly interesting.
Abstract
Chess is a competitive sport in the classical meaning of the word. One
of the most important factors for chess and sport competence is the
accumulated time of training. In order to obtain a high level of
competence, chess layers and athletes alike must spend up 10 years of
specific training.
In chess and classical sport energy needed for brain activity is first
derived from glycogen stores in brain, muscles and liver and later
from adipose tissue. Both, chess and classical sport rely on shared
energy from glycogen and fat.When the brain needs additional
energy, muscles and liver share energy with the brain. When
muscles need additional energy, brain complies with the request of
muscles. Energy expenditure, O2 uptake and CO2 production during chess
games are similar to those obtained during a marathon. Mental and
physical fatigue begin with similar metabolic states: deprivation of
glycogen. During competitive chess, athletes must be in good physical
condition.
Mental profiles of chess players and other athletes correlate with
processes such as attention, conflict control,memory, motivation and
recognition.
In chess there exists no gender-specific excellence; glycogen
availability, however, is less developed in female chess players.
In chess and in classical sports, the brain, spinal cord, nerves and
muscles cooperate in complete harmony. The brain commands everything:
in chess the figures, in sport the cellular receptors (baro-,
lactate-, gluco-, metabo-,chemo-, thermo-, respiratory-) “send”
signals via eyes or metabolic changes to the brain. The brain then
decides,what to do: in chess, the player moves a figure; in sports,
muscles react according to demand.
Physical exercise or chess must be defined by a motor activity
completely controlled by the central nervous system (CNS) in
combination with a specific competence. In chess as well as in
physical exercise, physical stress prepares brain to cognitive
stimulation.
With respect to biochemical, physiological, neuronal and psychological
aspects, chess is equals classical physical exercise and must be
recognized as sport.
Here is another article, "7 Surprising Health Benefits of Playing Chess", that lists various benefits that can are certainly physically related, and cites the sources.
