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They have an entrance examination and an interview, a quick google search will tell you all you need to know.
Correct me if I'm wrong:
Entrance exam has questions on math and economics (separately)
Economics is bachelors-level.
The math portion is high-school (up to the 12th grade) level, so most would not find it too tough.
The interview is also based on questions (which you are given to solve in some amount of time).
The website says they look at your past academic record but I doubt they would care if you can score well on their entrance tests.
The only think that matters is how well you can answer the questions in the interview and exam, which would reflect your analytic abilities and the depth of your exposure to economics.
Unlike UPSC, your personality and character take a back-seat (close to irrelevant), so they don't really need to "look" too hard for any sort of candidate, just see how you scored on the test.
Some people might say that depends on your aptitude but many also bring up how MSQE is not too hard to crack with enough practice (this is probably more applicable for DSE which is generally seen as "easier").
A small percentage of the batch in both ISI and DSE are always engineers (is what I hear and can see on their placement brochures) however these are usually the ones that are able to work hard and grasp a large syllabus quickly (is what I hear), not surprisingly they tend to be from IITs.
Also, here is a post by shar311, who seems to have been in a very similar situation to you:
"let me share my experience with dse and then you can get an idea. I passed out from an iit in 2012 and took to the course of civil services. had appeared for interviews but couldnt make it in 2012/2013. the biggest debacle was 2014 mains exam where i didnt find my roll number in the list. it was on 12th april to be precise. because of peer pressure, with batchmates travelling across the world, doing amazing stuff, i had to decide to get a formalised backup and then dse was one option in front of me. gathered all the courage and wisdom, started preparing for the entrance with no detailed exposure to the syllabus of the entrance in 3rd week of april. did some past years papers where this forum was of great help. there are some video tutorials which helped me in econometrics as reading gujrati was a bit boring. i had been working as well so could spend 3-4 hrs a day on prep. finally wrote the exam, and there was this one question of probability which somehow i wasnt able to solve. when the result came, i scored 38 marks just 2 short of making it which could have been possible had that question clicked (mainly because it was 0.1 or 0.01 percent which we took as 0.1 or 0.01 instead of dividing it by 100). but that's okay for now. i moved to singapore a few days later and as i see it, 2-3 months of rigorous prep is sufficient even without any coaching. religious practice of varian workbook, reading macro std books, gujrati i would prefer those lectures any day, and brushing up maths fundamentals would help you sail through the exam."
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