For 'proper' language, maybe, but for intelligibility, not so much. Especially when spoken.
"I want food", "Food, I want it.", "I am wanting food.", "Food for me; hungry.", "Want food.", "Me want food." Are all completely intelligible to most speakers, if many are not proper grammar. You can drop or add all sorts of articles and pronouns in there without really affecting basic intelligibility either.
The first three are grammatical, not so much the last three. I agree most speakers of English (native or otherwise) could figure out what someone saying the last three intends. But you're saying that this is a special fact about English. That if I attempt to speak in 'broken Spanish' or 'broken Japanese' and produce the equivalent of 'me want food' in Spanish or Japanese, that Spanish and Japanese speaker would just shrug their shoulders and say 'who knows what he means'?
It's a general property of natural language that speakers can produce ungrammatical sentences and yet be understood by other (perhaps more fluent) speakers. English isn't special that way.
I can't comment on Japanese, but broken Spanish can be confusing (to me) due to verb conjugations. Conjugations are also a major sticking point for new learners of the language since they have a big impact on meaning but can be hard to remember.
For example, changing a single letter in "quiero" ("I want") can have a big impact on its meaning by becoming "quiere" ("He/she wants") and "quieres" ("you want").
But you can't say "Food want me". Whereas in Old English, the grammar had so many markings that poets could weave distinct phrases together and still convey their meaning. In practice, that would still be awkward for typical speech, but it's cool all the same.
"Man chased the woman" and "woman chased the man" have completely different meanings in English. In many languages, switching around the two nouns like that wouldn't necessarily change the meaning, and in others you'd at least be able to pick out that something had gone wrong.
"I want food", "Food, I want it.", "I am wanting food.", "Food for me; hungry.", "Want food.", "Me want food." Are all completely intelligible to most speakers, if many are not proper grammar. You can drop or add all sorts of articles and pronouns in there without really affecting basic intelligibility either.