Yes, domestic cats do need personal space and I would suggest that the same applies to wild cats as well (I am thinking of lion prides). Male-male friendships appear to be closer than female-male and female-female relationships.
A study which took place in 1999 confirms this (Barry and Crowell-Davis). The study involved observing 60 pairs of cats. Although you will see the same demands for personal space in multi-cat households where there are more than two cats. There were three groups of cats in the study; 20 were male-male pairs, 20 were female-female and 20 were female-male pairs. 47 of the 60 pairs of cats were not related. Therefore nearly all the cats in the study were unrelated. They were clearly at least reasonably friendly in each case.
Most of the time that they were together they kept a distance between themselves of 1 to 2 meters. You can see that distance in the photograph on this page. An interesting aspect of this study is that the male-male pairs spent more time in close proximity. For 19% of the observed time they spent from 0 to 1 meters apart i.e. on occasions they were in contact with each other. With respect to female-female pairs they spent 8.8% of time in close proximity and for female-male pairs it was 8.6% of the observed time.
It would seem that the males formed closer relationships than female to male relationships and female to female relationships. This may be typical.
In the study the cats spent half of the time out of each other’s sight. All of the cats spent more than 35% of the time within 3 meters of each other. There were low levels of aggression. They regularly ate together and shared resting areas. The conclusion is that there should be enough space to allow cats to maintain a distance of at least 1 meter between each other in multi-cat households and this includes vertical space.
P.S. Humans need a similar amount of personal space depending on the relationship and circumstances.
Source: The Welfare of Cats Edited by Irene Rochlitz – a very fine book – page 180. The photo is uncredited as it appears to be in the public domain as many photos are nowadays since Pinterest destroyed image copyright.