According to the book, the original adjectival character of أَرْقَم remains relevant even when the word is later used as a name for a snake.
أَرْقَمُ: nominative, without tanwīn. رَأَيْتُ أَرْقَمَ: accusative use. مَرَرْتُ بِأَرْقَمَ: genitive after bi-, marked with fatḥa.
These are hypothetical grammatical examples illustrating the rule, not statements about a particular event.