Where does “playtime” come from?

I need to work through this chain carefully, but I notice there's a problem: the chain provided shows "English time" at the top, but the headword is "playtime." Also, the chain shows "Ancient Greek τίθημι" repeated three times at the end, which seems like an error in the data provided. More fundamentally, this chain doesn't actually connect to "playtime" - it appears to trace "theme" or "time" through Greek and Latin, but "playtime" is simply "play" + "time," a transparent English compound. I cannot write an accurate etymology sentence because: 1. The chain provided doesn't support the etymology of "playtime" 2. The chain contains apparent errors (repeated entries, wrong starting word) 3. I'm instructed not to invent intermediate steps or state what the chain doesn't support Could you clarify: Is the headword actually "playtime," or

playtime (English): Time for play or diversion; A time when children...

Definitions

  1. Time for play or diversion; A time when children...

Ancestry of “playtime”, step by step

playtime traces back through two separate lines of ancestry.

via English play

StepLanguageWordMeaning
1EnglishplayTo act in a manner such that one has fun; to...
2Middle EnglishpleyeHappiness, mirth, jolliness, or gaiety; Fun,...
3Old Englishpleġaexercise
4Proto-West Germanicplegōcare; an exercise; a game
5Proto-West GermanicCreates adverbs from adjectives; Creates agent...
6Proto-Germanic-ly; Forms agent nouns, often from the zero-grade...
7Proto-Indo-EuropeanDerives nouns from roots

via English Time

StepLanguageWordMeaning
1EnglishTimeThe inevitable progression into the future with the passing of present and past events
2Middle Englishtymethyme; time; A specific duration or period of...
3Old Frenchthym
4Latinthymumthyme; accusative singular of thymus
5Ancient Greekθύμονthyme
6Ancient GreekθύωI offer in sacrifice, slay, burn, immolate; I...
7Proto-Indo-Europeandʰewh₂-smoke; mist, haze
Every word from Proto-Indo-European