I have heard that, in former times, there was a very polite form of speaking in the form of, e.g., "the emperor liked playing to die" instead of "the emperor died". Is this true that there is a style of japanese in which people speak about playing to or pretending to do something for reasons of politeness?
It is true that a word that means 'play' is used to get the super honorific form (although you seem to have misunderstanding in that you presented
the emperor liked playing to die, which does not fit).
To get the super honorific form, you can attach
あそばす (which is a classical honorific form of the verb
遊ぶ that means 'play' when used as a main verb) after the verb stem (with epenthetic vowel
'die/disappear' (euphemism of
'die' (super honorific)
'study' (super honorific)
Generally, the strategy primarily used to honor someone in the Japanese language is to remove the volition from the person. Hence, referring to a person not by the personal pronouns
彼女 but by the locational demonstratives
どなた, or directional demonstratives
どちら, as if that person is not a person, is more polite.
られ, which initially only meant passive, came to be used to express honorifics because passive will syntactically remove the volitionality (agenthood) from the subject. The same with
なる 'become'. Becoming something does not need volition. Using
あそばす 'play', in my hunch, is along the same line. By adding this verb, it means that the act was not done under full serious volition or intention. In English, the same strategy is used to at least weaken the responsibility of the person doing something (although I am not sure if that is necessarily considered as being polite). For example, instead of saying
The US army killed some civilians,
Some civilians were killed (by the US army) implies less volition, hence less responsibility, of the subject.
In present Japanese, this form is used as 役割語 (stereotypical role words) for rich madams (often in imperative form). These are called あそばせ言葉.
'excuse me' (implication of stereotypical rich madam)