The description in the drawing isn't quite correct. The two vertical red-text Dimensions that hit the top edge [6'-0" and 5'-5"] are each shorter than the horizontal ones they cross over -- according to the description, those horizontal ones should be the ones deleted. If you really want to delete the red ones, can you refine the criteria? Delete the one of such a pair that meets the perimeter, perhaps? Post 4's text [not the description in the drawing] sounds like that, and it's true of all your red-text ones, but maybe it wouldn't always be.
As for determining whether two Dimensions overlap in that way, in the case of no-extension-line Dimensions like these, their DXF-code 13 and 14 entries [definition points] can be collected into a list, and (inters) can be (apply)'d to that list without the 'onseg' argument, and if there is a result that is not a (member) of the same list, then they cross but don't meet at ends. [It might be necessary to compare the result to each item in the list with (equal) and a small fuzz factor, rather than use (member).] The stepping through each Dimension and comparing it in that way with all others would seem to be the tedious part. Depending on the answer to the issue in the first paragraph above, it might also be necessary to compare them to the perimeter, which the User would presumably need to select unless it's always the only Polyline on its Layer, or can otherwise be tied down for the routine to find on its own.
Kent Cooper, AIA