The grammar of ～ておりやした
I was watching the さらい屋五葉 anime, and there was a phrase in one of the episodes: 子供と遊んでおりやした, which was translated as "He was playing with a kid." Could you please explain the grammar behind 遊んでおりやした? I know that 遊んで is the "te-form" of 遊ぶ, but could you please break down the rest for me?

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As kuma wrote おりやした　is an old Japanese in Edo period. You watched anime of Edo period. So if you use this old Japanese now, it will be very funny. And おりやした　is male phrase.

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「…やした」has seemed to start using from the Edo era and the merchants and workmen used this expression to the upper rank of the persons at that time like Samurai.

「おりやした」→ 「おりました」→ 「いました」
So, 「あそんでおりやした」= 「あそんでいました」

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Technically it is the same as 遊んでおりました, but spoken in more childish or [considered to be] 'cute' [in the world of anime] way. :)