The phrase "will have had" means something that has not happened yet, but after the event looking back one would be able to say "has had". This tense describes a past that will occur in the future, and is usually speculative or hypothetical in nature.
In this specific case, this statement "structural needs will have had a vital hand in shaping its form" means
"structural needs are vital in shaping its form", it's just put into a future tense because the building does not exist yet, but the author is supposing that when the building does exist, then these things would be true of the past.
I will simplify the tenses for you:
The building is hardly there to satisfy the needs of structure but, whatever its purpose or plan, structural needs will have had a vital hand in shaping its form.
The building is there to satisfy only minimal needs of the structure, if at all.
However, the structural needs are vital in shaping the form of the building, which has yet to be built.
Another example, "Once I finish this pancake I will have had 5 pancakes."
It's a sort of future retrospective tense, where one is talking about a past tense that has not yet occurred, but is expected to occur. In the case you asked about, it introduces the information that the building does not yet exist, or that some other related event is still yet to take place in the future.