First off, in the source sentence:
The kitchen’s window and door combination has an arch similar to that
of the brick-in arch elsewhere in the facade.
The possessive "kitchen's" does not modify "window", but rather "window and door combination". If one did use "kitchen" in this context the reader might well be led down the garden path to concluding that the reference was to a door/window combo similar to that that might be used in a kitchen (even though, in this case you could be talking about a bedroom).
And in the second source sentence:
[...] and an assortment of sweets soon cover a long table by the
kitchen's window .
What's being described is the layout of the kitchen. Thus a specific window is being referred to, and window is not so much a feature of the kitchen but rather a "landmark".
As with most things English, the rules are mushy, but the non-possessive use of "kitchen" to modify "window" implies a window of the type used in a kitchen, while the possessive implies a window which is "owned" by the kitchen.
There is plenty of room for both forms to be used, depending on context.
Best Answer
Some English verbs can be used in a verb + adjective structure. The copula, be, is obviously one (I am cold). Verbs used functionally purely as a link between the subject and an adjective (or noun: I am John) have been called link verbs by some, although some say this approach is unacceptably simplistic (see John Lawler's comments in the What are all the words that make up a complete list of linking verbs in English? string).
Verbs which link but also carry semantic weight (he became cold / she stood tall / the rose blushed pink) have been called link-like verbs.
The adjective does not really modify the verb directly as an adverb would. Consider the differences between 'rapidly' and 'cool' (one giving more detail about the process, one describing the final state of the referent) in The lava rapidly became cool. Another example: 'act stupid' can mean something different from 'act stupidly':
to act stupid (= pretend to be stupid) [Collins Spanish Dictionary].
'Play dead' etc are, however, perhaps better treated as inseparable idioms.