그 + Noun-은/는 = The aforementioned N / That N, where 그, "That" is a "referential The" (abstract, not in sight object)
그 + Noun-이/가 = The N indicated/ That N (there), where 그, "That" is a "indicative/identificative The" (concrete, pointed-out object)
This is why sometimes 그, is seen translated to "The" (an emphatic "The").
"That much" can only be used with non-comparable (absolute) adjectives like different, ideal, perfect etc. (i.e. adjectives that have no comparative and superlative).
높다 = high (comparative: higher; superlative: highest) is not an absolute adjective.
So it is incorrect to use "that much high".
그만큼 높다 = that (/so) high; as high as that
--> 그, used to refer to thing(s) physically close to the listener or to refer to some abstract (not in sight) matters (things or concepts) known to both interlocutors.
--> 저, used to refer to thing(s) physically at some distance away from the interlocutors. 저 always refers to things "visible" to the interlocutors.
"The" as definite article is never translated into Korean. For emphasis as in "The ... there", use "That". (* In English, "that" is known as the "emphatic the".)
그 나무는 그만큼 높습니다 = That tree is as tall as that.
There are 2 "그"s at play in this sentence. So there are 4 possible scenarios.
For the sake of argument, let's call "that tree", O1 and the other "that", O2; A, for "not visible, absent" and N, for "near Listener".
O1-A; O2-A (*your model)
O1-A; O2-N (*your model)
그 나무는 그만금 높습니다 = As for that tree, it is that tall (as tall as that) --> characterization of a specific tree. ( Focus is put on the characteristics of the tree, i.e. 'that tall' )
그 나무가 그만금 높습니다 = It is that tree which is that tall --> Identification of a tree of such height. ( Focus is on "the tree" which fulfils the given criterion. )