Can I watch movies I've purchased in iTunes on different Apple TV devices?

I thought I could log in to my iTunes while house-sitting at my brother's place, and watch my movies on his ATV. But it doesn't show me my recent purchases.

I always make a point of buying movies from my computer rather than on my own ATV so that I can watch them anywhere, and I thought that included being able to watch them on other ATVs if I sign into my iTunes account.

Apple TV

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