The special consideration given to the United Kingdom indicates to me that "Europe" here means actually "European Union" because geographically it wouldn’t need mentioning. Additionally the ministry is primarily interested in political entities, not geography.
As far as the general question goes, the borders of Europe have been pretty unanimously agreed upon for the past 150 years or so. It is a mixture of waterways and mountain ranges, indifferent to the political borders du jour, so that some countries like Turkey and Russia straddle the border to Asia. News to me was that also Kazakhstan’s west lies in Europe because the geographical demarkation — the Ural river — is not a national border.
I don’t know the answer for the general question, but to answer the sub-question: Turkey is included in the list of at-risk countries, according to the Indian Embassy in Ankara.
In view of the evolving nature of SARS-CoV-2 variant: B.1.1.529, new
guidelines have been implemented in India for International arrivals
which mandate all passengers from the Countries At Risk to be tested
for RT-PCR on arrival at the first points of entry into India. This is
to clarify that “Turkey” is included in the Countries At Risk under
the first group of countries, in the list i.e. Europe. Consequently,
passengers arriving in India from Turkey will be subjected to
additional measures of health checks, as notified vide Ministry of
Health and Family Welfare, Government of India Guidelines for
International Arrivals dated 28 September 2021, which can be accessed
here.
Credit:stackoverflow.com‘