How can we summarize the entire story of Shelley's Frankenstein just on the basis of the Gothic writing style since it is a Gothic novel?
Like many forms of genre novels, Gothic novels are defined by certain characteristics that are uniformly present. It is because of this that it might be possible to give a generalized and sweeping summary of a Gothic novel based upon its genre related "writing style" alone [although the term "writing style" is usually used to indicate a particular author's style of writing, not the characteristics of a genre].
First, typical core characters involved in a summary are the (often female) protagonist, the villainous (usually male) antagonist, and the Wanderer, and possibly the lost love. The protagonist must always fall in defeat before the antagonist, at least for a time, though some stories depict the protagonist's fall and doom as irrevocable, as does The Monk by Matthew G. Lewis. These are the characters who will be the agents of action in a summary of the plot that unfolds the conflict.
The plot reflects the Gothic novel ideology that Gothic novels portray the fallen world, fallen from grace and suffering from the separation isolating the world from the divine. Accordingly, the Gothic plot features a heroine who is by one means or another isolated from family and friends in a setting that shows the ruin that is part of the fall from grace--this ruin symbolically represents the condition of the physical world and the human condition.
In Gothic stories' general summaries, the isolated heroine faces the evil designs of the malevolent antagonist, who has suffered his own fall or is simply evil-spirited by nature. The protagonist attempts to flee the power and actions of the antagonist but either (1) cannot escape, as in The Monk, or (2) cannot escape without the help of a loved one as in Ann Radcliffe's The Mysteries of Uldolpho.
In Frankenstein, the general summary holds true, but follows the pattern of The Monk more than that of The Mysteries of Udolpho. Further, in the duality Mary Shelley creates, Victor Frankenstein is in a sense both protagonist and antagonist as he is the central character and the one who behaves villainously. Additionally, Shelley establishes him as the embodiment of both old ideology and new science. In another sense, the creature may be seen as the protagonist as he is characterized as naturally loving and gentle in contrast to Victor's natural heartlessness. Either way, the conventions of the Gothic are upheld as both Victor and the creature are trapped in decaying circumstances and fallen from grace. The end resolution is that there is no loved one to help either escape and each meets a final fatal end in doom.