The popular press is currently rife with speculation that emoji are becoming a global, digitally-mediated language. Sequences of emoji that function like verbal utterances potentially lend strong support to this claim. We employ computer-mediated discourse analysis to analyze the pragmatic meanings conveyed through emoji sequences and their rhetorical relations with accompanying text, focusing on posts by social media influencers and their followers on a popular Chinese social media platform. The findings show that the emoji sequences can function pragmatically like verbal utterances and form relations with textual propositions, although their usage differs from textual utterances in several respects. We also observed user innovations that make the sequences more language like, although there is not as yet a fixed grammar of emoji sequences. We characterize this emoji use as an emergent graphical language, with the caveats that it is not yet a fully-formed language and that the Chinese emoji language that is emerging is different from the English variety, and therefore emoji are not a universal language. In order to promote the further development of emoji language(s), we advance recommendations for emoji design grounded in linguistic principles.