Is Morse Code a Language?

No. Morse code is a code, not a language. It turns the letters of a language you already know into short and long signals, so .... .. is just the English word HI spelled out.

Code vs language

A language has its own words and grammar. Morse code has neither. It maps letters, numbers and punctuation to patterns of dots and dashes, and the international standard, ITU-R Recommendation M.1677, defines it exactly that way: a list of characters and the signal for each one.

That's why an English speaker and a French speaker can both send perfect Morse and still not understand each other. Same code, different languages.

Other alphabets get their own codes

Every writing system needs its own mapping:

Japanese uses Wabun code, which gives kana characters their own dot and dash patterns.
Russian, Greek and Arabic each have Morse alphabets for their scripts.
Chinese has thousands of characters, so the Chinese telegraph code gives each one a four-digit number, and the numbers go out in Morse.

Why it feels like a language

Learning Morse is a lot like learning to listen to a language. You build speed over months, and experienced operators hear whole words instead of single letters.

Hams also share a shorthand of Q codes and abbreviations like 73 (best regards) and QTH (location), plus prosigns. That lets operators with no common language swap basic details, but it's radio jargon spelled in ordinary letters, not a language of its own. For the bigger picture, see what Morse code is.