Without your receiving a response from the contact form, and there being no answer when I call the phone number listed in business directories online, let's see what clues we can find on the website...
There is a "submit a translation" feature. This is ambiguous since individual translations could contribute in a statistical way (i.e. enlarging the corpus) or in a rule-based way (i.e. add a rule matching this text). However, it seems rather that this forms a knowledge base with upvoting, downvoting & comments and is probably separate from the machine translation engine.
The site has existed since 1995. This means it probably didn't begin as a statistical system (which was not the norm at the time, to my knowledge). Even if it has changed since then, it may well contain elements of a non-statistical base.
Funny enough, BabelFish's main business appears not to have been this dinky little site, but human translation; in fact, their early descriptions of themselves forswear machine translation.
Many of the pages have been blanked, and ads appear if you disable your blocking extension. The company is probably defunct. The Wayback Machine also shows some hijacking at least once, not long before everything was blanked. I wonder if this barely functional tool and remnants of the knowledge base are kept online simply for ad profit, whether by the original owners or webmasters or hijackers.
- 2016's about page uses language indicating that they have no idea how common online translation is, suggesting that they probably are stuck in the past in terms of what machine translation is and can be.
- 2011's blog post on English-Latin translation is nonsense, but perhaps contains a hint in the claim that since Latin is "incredibly complex", online tools may not work for it. If this has any relationship to the reality of their technology, it would suggest a rule-based approach.
- 2011's blog post on English-Spanish translation is equally nonsensical and equally suggestive of a rule-based approach — again, assuming this "Jenn" has any knowledge of their technology.
Let's try out some standard phrases. A classic example mentioned on Wikipedia is to try "Japanese prisoner of war camp" and substitute different demonyms for "Japanese". This phrase is ambiguous; who's Japanese: the camp, the prisoner(s), or the war (possible in different languages' syntax)? The variations might be expected to be parsed identically if it's rule-based, but differently if it's statistical, since some countries will appear often in the corpus but others will have no precedent.1
|Japanese prisoner of war camp
||Camp de prisonniers de guerre japonais
|Ethiopian prisoner of war camp
||[Literally tried for half an hour but got "unavailable" messages]
I guess that's about all it's possible to find out if we can't even do heuristics.2
1 In 2013, when I last tried this out in Google Translate, it gave different syntaxes for the different countries. I see that the syntax is now much more stable, but the implied parsing still isn't identical; sometimes the demonym agrees with "camp" and sometimes with "prisoners".
2 Another example is to use an elision allowed in one language but not another. Again in 2013, I tried "I always will" in Google Translate, knowing that the French future tense must supply a verb. Sure enough, GT yielded "Je t'aimerai toujours" ("I believe I will always love you"), highlighting a weakness of statistical correlation. Now it yields "Je vais toujours", which preserves the elision but is not very good as a whole sentence in French, and offers the alternative "Je le ferai toujours" ("I will always do it"), which is the best one could expect without context.