Why was William Tyndale burnt at the stake?

The trivial answer is he was executed for being a Protestant. The deeper answer is we aren't quite sure, but he had gained some powerful enemies.

There was a lengthy list of charges read at his trial. While I don't have access to the full list, the first 7 appear to be unrelated to the actual act of translating The Bible into English, but rather are simply a list of typical Protestant beliefs.

First, he maintains that faith alone justifies.

Second, he maintains that to believe in the forgiveness of sins, and to embrace the mercy offered in the gospel, is enough for salvation.

Third, he avers that human traditions cannot bind the conscience, except where their neglect might occasion scandal.

Fourth, he denies the freedom of the will.

Fifth, he denies that there is any purgatory.

Sixth, he affirms that neither the Virgin nor the saints pray for us in their own person.

Seventh, he asserts that neither the Virgin nor the saints should be invoked by us.

The court in question was part of the governmental machinery of the Holy Roman Empire, which was officially Catholic, so being a Protestant was grounds for execution. Of course this was a "court" where the outcome was predecided, so what the judge told the gallery at the start is probably the most relevant.

He has been arrested for many great heresies; his chamber has been searched, and prohibited books have been found in great numbers; and he has himself composed many treatises containing heretical opinions, which have been widely circulated.

So the simple answer would be that he was executed for being a Protestant.

However, that answer is too simple, because the HRE at the time was in the middle of the Protestant Reformation. Likely half the empire was Protestant at the time, most of whom were not being arrested and executed, so its reasonable to ask why Tyndale got special treatment.

For this it would be useful to look at how he came to be arrested. An English agent was sent to infiltrate his circle, and that agent betrayed him to the HRE authorities for arrest.

Who hired this agent? We aren't sure, but we can make some guesses. The English clergy at the time was splitting from the Catholic Church, but was still itself quite anti-Protestant. So most historical speculation has landed on that quarter. So in this case the cause is likely to be not that he was a protestant, but that he was a vocal and influential English Protestant.

Part of their anger was certainly over the Bible Translation. There's a fun story about the English Church buying up every copy of the first edition just to burn it. The story goes on that publicly burning scripture was not a good look for the Church, while his publisher happily took their money and used part of it to finance printing a second edition.

King Henry himself is also a possibility. At first the King was a fan, after reading The Obedience of a Christian Man, which was pro-secular authority. However, Tyndale argued against Henry's divorce, which served to put him in the same political hitlist as Thomas More. There are accounts of the King sending agents to attempt to capture Tyndale, and appealing to the Emperor. So it certainly would be within character for it to have been a Crown agent organizing the job. At the absolute least, whoever did it knew they wouldn't get any pushback from the Crown over it. At most, its possible what actually got him killed was arguing against King Henry VIII.

Taking all this in, and looking back at the (according to my searches, quite common) claim that it was specifically the English Translation that got him killed, I don't think that's quite accurate. However, it isn't wholly inaccurate either, as that translation was the culmination of his life's work, and his life's work was certainly what got him killed. So if you hear someone saying it was the translation, I wouldn't bother to "well actually..." them over it.