If you want to take this to its logical conclusion, then language is nothing but a fixed set of "alphabet", and a set of rules that generate infinite strings from this alphabet in some meaningful combination.
Alright, I will start: I am fluent in the language of traffic signs.
The confusion isn't coming from conceptual similarity, though. It's coming from the use of the word "language" which has multiple, distinct connotations. Traffic signs are never referred to as "language." Both spoken and programming languages are.
I'll bet that if you talk to designers and road layout experts, they'll freely talk about the "language of traffic signs". I'd also hazard a guess that people who are not programmers or familiar with how it all works would not refer to what we work with as a language, but as "code", "mathematics", "bits and bytes" etc.
Alright, I will start: I am fluent in the language of traffic signs.