I thought he was nit-picking the OP’s use of “non-English speaker” vs. “non-native English speaker”. 
I dunno. If you take a Texan and a New Yorker, they sound as different as a Yorkshireman and a Liverpudlian. IMO.
FWIW, a good-sized part of Phil Hartman’s SNL audition was his impression of someone doing an impression of Jack Benny and John Wayne and Jack Nicholson – which was, of course, perfectly accurate despite the guy speaking fluent German throughout.
I’m not sure if that’s necessarily true, butl Liverpool is only about 50 miles from Yorkshire (at it’s nearest point in the West Ridings).
Also from what I understand New York and Texas dialects are pretty much at the different ends of the spectrum under the usual catergorization of Amerin English dialects, whereas in the usual classification of English dialects Scouse and Yorskhire dialects are regarded as relatviely close.
That being the case, I think there must be dialects/accents of English that non-English speakers would find difficult to recognise as English at all, for example, Northumberland, Aberdeen, or Cornish?
I think it depends on how well you know a language and its different accents. In English I can definately hear the difference between British and Amarican. I probably also would be able to identify Irish, Scottish, Liverpudlian, Cockney, Welsh (love the Welsh accent) from this side of the pond and ‘Southern’, New Yorkish, Bostonish and sometimes Canadian (Manitoba stands out) from the Wetern Hemisphere. Mostly because of movies and TV though.
I have the same in most other foreign languages I speak (German and a few others), but strangely enough not in French…
This discussion is very interesting and all, but 90% of the responses don’t address the OP who asked if native German/French/Spanish speakers could distinguish Brits and Americans when they are speaking German/French/Spanish. Although, to be fair, this could prove difficult if you can’t even tell them apart when they’re speaking English.
Even non-British native English speakers would struggle with those I think. And you can safely add Glaswegian to that list. I lived in Glasgow for a while. It was three weeks before I understood a word anyone was saying.
Of course, the guy named Chronos would post this.
I’m open to being corrected, of course, but I don’t believe that the OP intended the question to be interpreted this way.
State ay you. Sakes man! Guy’s a muppet.
My husband is from Switzerland and is a native speaker of Schwyzerdütsch. I am very used to it, and so I can tell when someone is speaking English, if their native language is Deutsch or Schwyzerdütsch.
It just takes a trained ear.
This might have some distant bearing on the subject. Right out of college, I went along on a group tour of Europe set up by a professor from the University of Illinois. As a group tour, we flew on a charter flight to London, then got taken around the Continent by bus. Parisian bus driver, and one our group was a student from Montreal. They spoke to each other in French, naturally, and I at least couldn’t understand any of it. Anyhow, there is just no mistaking the difference in French spoken by a Quebecois and a Parisian. That Canadian accent came through very clearly.
As part of the tour, they took us to a nightclub show in Paris. Pretty dancers, of course, and a comedian doing his routine - in French, of course - and it wasn’t hard to figure out which one of the groups in the audience he was making fun of. Us, of course. Particularly when part of the routine consisted of looking at us while speaking French with a very American accent. Mid-west ‘standard’ American, as I recall, no special attempt to make fun of Texas or New York. Otherwise no big deal, because making fun of people is what comedians are supposed to do. Whatever it was he said.
Numpty. 
Rocket
Well, to be fair, they are tricky even for people from other parts of Britain, which is the point I’m driving at about the diversity of accents that comprise ‘British English’ (granted, some of it is dialect not accent), and the difficulty of saying very much in a general sense about the collection.
Nor did I, but on re-reading, I’m not sure.
In Spanish, I’d say there’s differences but frankly most of the traits are common whether the person speaking is from Auckland, Glasgow or Philadelphia. Often, any regional differences they bring over from English are overlaid by those of their own Spanish - same as we are taught and try to speak either “American Newscaster” or “Received Pronunciation” (and often end up with “Spanish dishwasher in Dublin”), Anglos speaking Spanish will usually have been taught Mexican, Argentinian or Castillian. Any specific things a person does which are not part of the general “anglo speaking Spanish” accent nor of their Spanish dialect, we attribute to the person specifically. Take into account that your average SFL-with-ESL also doesn’t know enough about English dialects to be able to tell whether someone is from Brooklyn, from Manchester or from Florida based on how they talk - we’re much more knowledgeable about the two spelling varieties (which impinge directly on our ESL grades) than about which accents exist in English outside of language tapes.
There’s a few notable exceptions to the “I can tell whether someone’s first language is English, French, Italian… but not from where”: the kind of people who speak English like they have a burning potato in their mouth don’t drop it when switching to Spanish, and we know that one happens to be an American accent.
ETA: most Americans appear to recognize my own aksent not as “Spanish accent” but as “where the heck is she from accent”, because it’s not given by the varieties of Spanish they’re used to encountering (which will vary by US location), but by one that’s very close to Castillian. In the rudest cases, I’ve had to show my passport because the person in question refused to believe my accent could be “from Spain”.
Hmm, yes, I see what you mean.
I’ll just throw in a question here because it doesn’t seem worth its own thread. Cinemax just produced a series called Strike Back, in which they cast an Australian actor as an American soldier, and an American actor as an English soldier. I would have expected the opposite, everything else being equal (which it probably wasn’t). But to my ear, an Australian accent is a lot closer to an English accent than an American one. Am I imagining this?