"English hasn't got a (unique) alphabet, it shares the Roman alphabet with various others, so perhaps English isn't a language."

English has been using the same alphabet for very long time. It's unique inasmuch as it's different from Sanskrit, Chinese, Russian, Greek and so forth. It is definitely counted as a language.

I was thinking about Batak, which contains many Indonesian words, but has it's own alphabet. The same goes for Bugis.