Why can people, who have their eyes closed, sense objects that are
approaching but not yet touching?
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Extrasensory perception isn't a legitimate phenomenon, demonstrated by
the lack of scientific evidence for any such claims: random individuals,
if tested to discover the qualities of hidden objects or images that
were shown to a different individual in a separate room, cannot
accurately determine above random chance those qualities. Even people
who claim to have the sensitivity score about random and make claims
about how the scientific rigor of the environment or lack of belief
reduces their power.

This is because, as has been shown by studies which miss a control or a
piece of information or otherwise "leak" data to the participants or
even the experimenters (by a failure to "double-blind"), people (esp.
those who claim to have ESP) are very good at subconscious inferencing
and develop senses about "impossible to know" knowledge from this kind
of data leakage.

Walking around in a room with one's eyes closed is much more leaky than
any of the scientific experiments on ESP. The floor can have a slight
grade towards objects, especially large heavy ones in older buildings.
The memory of a person about room structure and similar inferencing can
allow for internal spatial mapping to readily develop. Even the sound of
footsteps echoing off of objects (similar to echolocative skills which
certain blind communities have been able to develop) can generate clues.

The human brain is designed to be hypersensitive to spatial information
regardless of the visual component, so the innate ability of an ordinary
person to wander around a room with their eyes closed is unsurprising.