Why is the word "calculus" used to describe systems of logic and computation?
The word calculus comes from the Latin word for limestone, because limestone pebbles were used for counting; you may have a renal calculus: a kidney stone$^1$.

In mathematics, the word is used to describe any system in which symbolic expressions are manipulated by fixed rules$^1$, so we may speak of tensor calculus, vector calculus, predicate calculus, $\lambda$-calculus and integral and differential calculus$^2$. The latter two are related to the former in the sense that both are sets of rules for manipulating expressions. Running a Google Books ngram search on these words, approximately 1890 was the first year in which both "vector calculus" and "tensor calculus" were mentioned, and they have been in frequent use ever since.$^3$

The reason that to you, these systems seem to be using the wrong meaning of calculus is probably that you grew up associating calculus with differentiating and integrating real-valued functions, but this is a bias.

References

[1] Wiktionary page for Calculus

[2] Wikipedia Disambiguation page for Calculus

[3] Google Books search for integral, differential, vector, tensor calculus