I went through both Napoleon Bonaparte's tactics and that of Gustavus Adolphus. Both brought brand new tactics to the battlefield and elevated their nations to great power status. Napoleon's wars caused neighboring powers to reconsider and adopt their tactics, planting the roots for Prussian Military restructuring and the German Staff System.
Gustavus Adolphus, however, did not have a similar impact, despite being given the title "Father of Modern Warfare".
In the event that I am sorely mistaken, did Gustavus Adolphus trigger a similar level of military restructuring? Were there any European Military that actively implemented his changes?
I would argue that the basic premise of the question here is wrong. Napoleon's military reform did not plant the roots of the Prussian Military structure or the German Military Staff because that was done by Frederick William in 1640 and in all likelyhood heavily influenced by the reforms of Gustavus Adolphus and the success enjoyed by the Swedish Empire at the time.
It was Frederick William who reformed the Prussian army, creating the first real non-mercenary army of Prussia. It was he who introduced merit based promotion for the officer corps, it was he who introduced a tradition of trusting the officers and general staff to plan and execute a battle to achieve the goals he would set forth, basically mission type tactics.
Did Napoleon influence the Prussian army too? Sure, like and truly great general he influenced the armies of every nation he ever took on in battle, but so did Gustavus Adolphus 200 years before him. However, the social structures in the early 17th century were much more rigid than they were in the early 19th century which may lead to the reforms inspired during the Napoleonic era to be more visible.
Anyway, I wrote a long post on the reform of the Prussian army like two years ago. Here it is.
So first off, it's important to understand the difference between an RMA and a Military Revolution (MR). An RMA is a shift in the nature and conduct of warfare, generally instigated by technological advances, and which leads to a reorganization of military institutions, reconceptualization of doctrine, and new application of military technology. It is specifically limited to military organizations.
RMAs often occur as components of a broader "Military Revolution", which is a social-political shift that fundamentally changes the nature of war. So, unlike an RMA, which only affects military institutions, an MR is a change that is also affecting society itself.
This is important to understand before answering your question, because the Swedish reforms were an example of an RMA that occurred as part of a broader MR in the 17th Century that saw the creation of the modern state and modern military institutions. Many of the European powers at the time underwent institutional, political, and tactical reforms that contributed to a reshaping of how war would later be fought.
The French Revolution was itself an MR, with its associated RMAs being the levée en masse and the broader national political and economic mobilization, as well as the Napoleonic style of warfare which focused on the annihilation of enemy forces.
If you want to read more about MR/RMAs, I would suggest:
MacGregor Knox & Williamson Murray, The Dynamics of Military Revolution: 1300-2050
Colin S. Gray, Strategy for Chaos: Revolutions in Military Affairs and the Evidence of History
Jeremy Black, A Military Revolution? Military Change and European Society 1550-1800