It is certainly correct grammar. It may be redundant in some situations, but not always.
The village of Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch is usually abbreviated to Llanfairpwllgwyngyll, or to the short abbreviation Llanfair PG.
It can also be used to indicate that an abbreviation is considered short (by the standard of abbreviations)
MP, BBC and c. (for circa) are all short abbreviations, unlike the text slang "IITYWIMWYBMAD" which means "if I tell you what it means, will you buy me a drink"
So it is grammatical. It may be redundant. The redundancy may be on purpose, to contrast or emphasise a point. In this case, it is saying MP is an abbreviation for Member of Parliament, and this abbreviation is particularly short.