That answers quite a lot of thoughts I've had about texturing. Thanks for that ;DAssuming a texture map of 1024x1024 then each square of that UV map would be just a tad bigger then 100x100 pixels.
As the area you have outlined is 1 square wide and about 4 squares high you are looking at a 100x400 pixel density on your object.
On a 23" monitor with a resolution of 1920x1080 there are about 96 pixels to the inch in both x and y. Therefore, if your object is larger then 1x4 inches you will have pixel stretching.
Furthermore, looking at the texture map the object is unfolded and the largest single side is getting 1x1 texture square or about 100x100 pixels or about 1x1 inch without stretching on a 23 inch 16:9 monitor.