Thanks for bringing this up.
No, the information in the paragraph is incorrect. The most obvious mistake is the year of introduction - 1853 - which is wrong and even nonsensical. The first public railway in the country was opened in April 1853 in Bombay.
Delhi did not have any railways till 1866. The route to Lahore (via SRE) was opened by 1870 and the Delhi-Panipat-Ambala route was opened only in 1891. There is absolutely no possibility of having any train from Delhi to Karachi in 1853. Both places didn't even have...
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railway tracks then!
In fact, there were no dedicated trains between Delhi and Karachi at anytime in history. Passengers always had to change trains at Lahore.
However, there was a train named the 'Flying Mail' which used to run between Delhi and Amritsar until the 90's. This train was cancelled and the Shaheed/ Saryu-Yamuna expresses were extended to Amritsar from Delhi, running roughly with the same schedule as the old 'Flying mail'.
However, contrary to the article's claims, the Flying mail never went to Karachi. It was introduced after independence and was terminating at Amritsar right from it's introduction. It was introduced shortly after the formation of NR in 1952. At that time, it was just called 'Amritsar mail'. It was renamed to 'Flying mail' sometime around 1959.