The economist/political scientist meaning of "animal spirit" was first introduced in 1936, 46 years after the translation you linked.

However, "animal spirit" dates back to the Roman period. The 3rd century physician Galen described the "spiritus animalis" as a life force seated in the brain that causes the body to move through the muscles; sort of like a medium for consciousness. Though in Latin, "animalis" means "of life" (or more literally, "of breath")^1^.

Descartes popularized this 17th century, and this phrase was translated accurately into German as "Lebensgeister". See this German dictionary entry from 1793, or more explicitly this one from 1904. However, in English the "animalis" part wasn't translated.

This notion became associated with vitality across (western?) Europe, which is why in English we can say someone "is very spirited today", and in German someone would say that person has Lebensgeister. Or also how someone can "have the right spirit".

So when Marx says alienated labor saps your Lebensgeister, what he's saying is probably just the informal observation that it's draining your spirit. But someone with a more formal philosophical education might naturally have read "Lebensgeister" as a reference to Descartes' formal idea, which in English had always been called "animal spirit".

^1^ this is a translation of the Greek concept of pneuma psychae; literally "psychic breath", though more properly understood as the spirit of the mind. This in turn can be traced more vaguely to the ancient Egyptian concept of "Akh", the part of the soul that governs the intellect, and more generally to the Egyptian concept of a soul being made of distinct parts each responsible for maintaining different parts of the person.

The concept of Akh appears in the old kingdom, though if you've ever heard it before it would be as the Pharaoh Akhenaten, whose name means "mind moved by Aten, the god of the disk of the sun". Akhenaten tried to make Aten the monotheistic god of Egypt.