Among the government officials at the time and historians nowadays it was and is widely agreed he was impulsive, fickle, out of touch with reality, blunder-prone, and diplomatically inept. How much his influence was felt in policy is another question that's debated quite a bit among historians. I'm not an expert in this field, but I had a brief look and this was what I found, though the historiography is bound to be more complex by now.

Since this question ties into the reasons for WWI a lot, it's covered to an extent in Christopher Clark's recent well-received book The Sleepwalkers which I looked to for this, where he emphasises the anti-Bismarckian faction of the Foreign Office being the decisive factor in nudging the post-Bismarck Chancellors and the Kaiser away from Bismarck's web of alliances.

Leo von Caprivi, the first post-Bismarckian chancellor and Prussian foreign minister, had no experience in foreign affairs. Caprivi’s epoch-making decision not to renew the Reinsurance Treaty was in fact driven by a faction within the German Foreign Office which had secretly opposed the Bismarckian line for some time. Led by Friedrich von Holstein, [...] It was Holstein, not the chancellor or the imperial foreign secretary, who determined the shape of German foreign policy in the early and mid-1890s. Holstein could do this in part because he had excellent ties both with the responsible politicians and with the coterie of advisers around Kaiser Wilhelm II [...] Friedrich von Holstein, Count Philipp zu Eulenburg, the Kaiser’s intimate friend and influential adviser, and even the ineffectual chancellor Hohenlohe became adept at ‘managing the Kaiser’. They did so mainly by not taking him too seriously.

So there's two answers to your questions here: The Kaiser wasn't, according to Clark, the decisive factor here, but he was also considered thoroughly incompetent and failed to be "his own chancellor".

The third point underlying this is that Bismarck set up a fragile web of alliances by using a unique position at the center of government, where he de facto in personal union combined several offices to shape foreign and domestic affairs. Thus his departure left a structural vacuum rather than just a role to fill, in which different factions jostled to make their influences felt. To what degree that vacuum was able to be filled by the Kaiser is, as far as I can tell, a matter of dispute. His relationship to chancellors and ministers often consisted of them trying to rein him in. While this was something the more liberal parliamentary parties demanded on principle, the Kaiser was always being targeted for influence by ministers, and more and more efforts towards controlling his public appearances were expended over time. Chancellor Bülow sought to strictly "manage" the Kaiser from about 1897 onwards. However, the chancellors following the dismissal of Bismarck initially sought to portray the Kaiser as the decisive authority, particularly Bülow going further than most by calling himself a "tool" of the Kaiser's wishes (which turned out to be ironic). This ended by the 1900s due to the Kaiser's blunder-proneness, and after the Eulenberg and Telegraph affairs from 1908 onwards, his influence receded strongly into the background.

However, this doesn't mean his influence wasn't felt: In the 1890s Eley and Röhl argue he most made his influence felt. He also strongly supported e.g. Tirpitz' naval policies (contributing strongly to the arms race in the leadup to WWI, both a diplomatic and military precondition for it), and more generally put in place ministers he thought would please him. John Röhl argues he sought to maintain control by using what Norbert Elias termed "kingship mechanisms" - i.e. divide and conquer among courtly politics, making people scared to propose things they knew would displease him, as he would fire them.

All of this is insufficient to really tell the story of how Imperial Germany made its decisions, given it totally ignores social history and broader political trends, as well as the public perception and social authority of the Kaiser. Further, it's a surprisingly complex question to determine how much weight his actions had, where they can be placed on the spectrum between "none at all" and "single handed authority", both of which almost certainly overstate their case on any matter. That said, while the article is obviously making a point historians would refrain from making like that, it's not at all wrong in that Wilhelm II was perceived among officials as incompetent and is retrospectively judged as incompetent by standards of consistent, strategic thought and implementation of policy.

Sources:

Christopher Clark, The Sleepwalkers (2016)
Geoff Eley, 'The View from the Throne: The Personal Rule of Kaiser Wilhelm II', in The Historical Journal (1985)