We do accept "How many people did he promise that to." and I added "To how many...".
But according to https://www.oxfordlearnersdictionaries.com/definition/american_english/promise_1 all of "promise somebody something", "promise something to somebody" and "promise somebody (that)" are possible. The "to" before "somebody" should not be necessary, although some reports claim otherwise.
Unless you parse it that he promised the people to some that...
If you promise someone something, you tell them that you will definitely give it to them or make sure that they have it.
In 1920 the great powers promised them an independent state. [VERB noun noun]
The officers promise a return to multiparty rule. [VERB noun]