Card is slightly odd naming indeed.

Criticisms aside (sigh), according to Wikipedia, the term was introduced when proposed by mostly Googlers, with the original paper [0] submitted in 2018. To quote,

"""In this paper, we propose a framework that we call model cards, to encourage such transparent model reporting. Model cards are short documents accompanying trained machine learning models that provide benchmarked evaluation in a variety of conditions, such as across different cultural, demographic, or phenotypic groups (e.g., race, geographic location, sex, Fitzpatrick skin type [15]) and intersectional groups (e.g., age and race, or sex and Fitzpatrick skin type) that are relevant to the intended application domains. Model cards also disclose the context in which models are intended to be used, details of the performance evaluation procedures, and other relevant information."""

So that's where they were coming from, I guess.

[0] Margaret Mitchell et al., 2018 submission, Model Cards for Model Reporting, https://arxiv.org/abs/1810.0399