Yes, but no, but yes.
So, the Japanese people had a concept of cultural supremacy around the so-called "Yamato race". This 'Yamato', 大和, most typically associated with the World War II era super heavy battleship of the same name, is an outdated Japanese demonym, i.e. a word that in Japanese refers to Japan as a country, and more broadly to Japanese culture and the Japanese people.
So, in effect, the exaltation of this supposed 'Yamato race' is indeed a self-centered thought of racial supremacy in which a national ideology seeks to elevate its country's dominant ethnic group into a perceived spot of absolute superiority over all other ethnic groups. This, broadly, is equivalent to Hitler's and Rosenberg's models of the Aryan master race in Germany.
Herbert Bix writes as follows in his award-winning Hirohito and the Making of Modern Japan, an absolutely essential history of Showa Japan and particularly its emperor that I can without reservation suggest to anyone interested in the Hirohito period of Japanese history, and specifically in World War II (the book focuses mainly on the emperor's role in Japanese politics 1923-1945):
[Army Minister Araki's] two main rhetorical devices were the “great mission” bestowed on the “divine land” by the gods, and the hostile efforts of the Chinese and the Western powers to isolate Japan and prevent the “Yamato race” from realizing its sacred destiny, “secur[ing] peace in the Orient.” Later in the film ["Japan in the National Emergency" (1933)] Araki defined Japan’s role more concretely, seeing it as both strategic and cultural. The task was “to create an ideal land in East Asia,” which meant constructing Manchukuo and there realizing a harmony of the races. In effect Araki presented imperial aggrandizement as an idealistic effort to realize an antiracist utopia in Manchukuo.
[Bix, p. 273]
You'll notice that this excerpt speaks of 'harmony of the races'. The Japanese would have never spoken of themselves exclusively as racial supremacists that wanted to create a Japan-focussed world order, but they always stressed the 'harmony' between the ethnic groups. There is even something to be said about a cultural admiration (or inferiority complex) towards the Chinese, the culture of which was foundational to much of Japanese culture - a stark contrast to the war crimes later committed by Japan in China in the 'Fifteen Years War' of 1931-1945. This is very much similar to the 'separate but equal' idea that you might see in United States history in relation to the segregation of African Americans, but more diplomatically than domestically focussed. To Japan, western influence was a very useful scapegoat to base a national ideology of continental liberation around. The wars waged against European colonial powers could be easily framed as national liberations of the likes of Indonesia, India and others - and indeed, Japanese puppet regimes and volunteer soldiers from these regions fought on the side of the Asian Axis Powers at various points during World War II.
This Yamato racial ideology, on whose ethnic homogenity and purity Japanese nationalists had prided themselves (see Bix, p. 575), is in praxis different from Aryan race ideology in Germany, and in fact different from all western fascisms, by one specific national difference: the Japanese aren't white Europeans.
'Well, what does that matter?', you ask. It changes the political reality in which the proponents of the racial ideology had to act on the world stage. In western majority-white countries, the dominant racial supremacy ideologies were seemingly confirmed by the fact that white ethnicities and their nation states - the UK, the USA, France, Germany, Italy, Russia, Spain, Portugal - had conquered and subjugated much of the world, and the members of other ethnic groups with them. As a result, the Japanese racial supremacists had to deal with a world in which there was not only a lack of confirmation of their racial and cultural ideology, but also a world in which another ethnic group was clearly dominant, thus going against the Japanese ideology.
This resulted in a vastly different foreign policy approach of the Japanese government in relationship to its racial ideas. Whereas Nazi Germany kept its racial terror mostly domestic (at least until 1939) to avoid unnecessary foreign interventions while perfectly fine with the position of white Germans in the world justice systems, the Japanese Empire had an uphill battle to fight on behalf of ethnic Japanese people, particularly as it relates to the United States of America.
You see, the United States had just passed immigration laws discriminating against the "Yellows", and Japan in 1919 sought to amend the League of Nations founding charter with a clause on racial equality - certainly nothing that Nazi Germany would have ever done. This advance was rejected, primarily by Australia, where a 'White Australia' policy was active (see Henshall, p. 109) and the United States, the political elite of which feared domestic political advances of non-white minorities. It wouldn't have made a difference either way, as the United States ended up declining membership in the League, but it might give the impression that the Japanese fascists were more racially egalitarian than the American liberal democrats. Of course, neither of these were racially egalitarian to any significant margin, but the Japanese were in the ethnic group that was designated inferior, and they had to first catch up to the globally more powerful ethnic group before they themselves could designate other ethnic groups as inferior. Japan never cared about the equality of non-Japanese ethnic groups (see Bix, p. 590).
So, in practice, the racial theories in Japan had to be approached vastly differently than those in Nazi Germany. The Nazis' ethnic group was racially already on top - after all, the Nazis claimed many successes of other countries, including the UK and USA, as proof of the supremacy of the Germanic race. The Japanese could not do that.
But there were many parallels as well: The Japanese outlawed marriages between ethnically Japanese colonists in Korea and Manchuria with the local Korean and Manchu/Chinese peoples, to avoid dilution of the Japanese gene pool (see Hastings, p. 61), whereas the German version of such laws, the Nuremberg Racial Laws, were primarily aimed to prevent marriages between Germans and Jews and to specify the state of Jewishness of particular citizens. Both ideologies preached the existence of a culturally shared spirit, the Japanese version of which was the Yamato damashii, the Japanese spirit (see Bix, p. 52). And then of course there is the aggressive foreign policy aspect of both countries, both of which justified their rampant militarism with the need to protect their dominant ethnic group's future. The German Lebensraum policy was exactly mirrored by Japan's Hakko Ichiu, and in fact, many proponents of Hakko Ichiu were actively inspired by Lebensraum ideology (see Henshall, p. 117).
I'd be glad to answer further questions, but let me draw a partial conclusion at least.
Japanese racial supremacist thought of the Showa era was similar to its German counterpart in its prescription of a national mysticism based on the nation's dominant ethnic group, in the ideological sanctification of racial purity turned into active racial discrimination in domestic policy, and of course in its advocacy for aggressive foreign policy militarism for the purpose of the extension of the dominant ethnic group's 'living space'.
In actual policy however, Japan, due to the state of world diplomacy hugely favoring white European nations, had to politically and diplomatically act completely differently than a racially supremacist white European nation would have had to. This is most exemplified in its (completely self-interested) advocacy for a racial equality clause at the Versailles negotiations 1919 and its diplomatic opposition to American and Australian white supremacy systems in the 1910s and 1920s.