It was still Japanese. So it's not like a completely different language. The problem many people had with it was that it used very ritualized and formal form of the language. For an example of something similar in English there is a parliamentary body in the UK known as the House of Lords. However the full proper name of that body is The Right Honourable the Lords Spiritual and Temporal (of the United Kingdom, etc.) in Parliament Assembled. The speech tended to use these types of very formal names. It also used types of speech that had fallen out of use in everyday use. Imagine a speech in English where thee and thou are used a lot, where instead of saying 87 the speaker says four score and seven, etc.

The authors of the speech also took great pains to make the emperor sound as dignified as possible, and to avoid bluntly saying things like we surrender. Instead they used circumlocutions and said We have ordered the acceptance of the provisions of the Joint Declaration of the Powers. Some of this was normal court speech. Much like modern US legislation will often use words like insomuch which have fallen out of common everyday American use, court Japanese did tend to use extra-flowery language. But not so much that it was unintelligible. The surrender speech however went overboard even for the flowery language of court. Take this final paragraph:

Unite your total strength, to be devoted to construction for the future. Cultivate the ways of rectitude, foster nobility of spirit, and work with resolution – so that you may enhance the innate glory of the Imperial State and keep pace with the progress of the world.

That is supposed to be a very good translation of the feel and flavor of the original in Japanese. Imagine a US president used these exact sentences in a similarly momentous speech, and you'll understand the Japanese confusion. "Cultivate the ways of rectitude?" Most English speakers hearing that would be confused. The Japanese were similarly confused.