Name of the Video?

There were several films based on the Hans Christian Andersen tale "The Little Match Girl" first published in 1945.  I don't know what you consider "short", but I will list the films I can find.

https://www.imdb.com/title/tt0093425 from 1987.

https://www.imdb.com/title/tt0495375 from 1974.

• The Little Match Seller (1902), a short silent film directed by James Williamson
• The Little Match Girl (1914), a 9 minute long silent film directed by Percy Nash.
• The Little Match Girl (1928), La Petite Marchande d'Allumettes), a 40-minute silent film by Jean Renoir.
• La Jeune Fille aux Allumettes (1952), French director Jean Benoît-Lévy's film version, includes a brief dance sequence with ballet star Janine Charrat.
• Den lille pige med svovlstikkerne (1953), Danish film director Johan Jacobsen adapted the Andersen story to a short film, starring Karin Nellemose, Françoise Rosay, and Agnes Thorberg Wieth. The film competed for the short film prize of the 1954 Cannes Film Festival.
• La vendedora de rosas (1998; Little Rose Selling Girl), directed by Víctor Gaviria, is a Colombian movie about homeless children victims of solvent abuse, loosely based on "The Little Match Girl"; it competed for the Palme d'Or at the 1998 Cannes Film Festival.
• Resurrection of the Little Match Girl (2003) is a Korean movie.
• Matchstick Girl (2015), a modern adaptation short film set in the UK, was produced and directed by Joann Randles.
• Match Shojo (2016), a Japanese adaptation of Sanami Suzuki's manga starring Sumire Sato.

Animated films

• Color Rhapsodies (1937), a Charles Mintz studio color cartoon adaptation set in 1930s New York City, directed by Arthur Davis and Sid Marcus, and considered among the studio's best films. It was nominated for the 1937 Academy Award for Best Short Subject (Cartoons), though it lost to Disney's short The Old Mill. This version of the story is slightly different from Andersen's story, specifically near the end.
• La Tartelette (1967), a Jacques Colombat short film inspired by Andersen's story, with a black humour twist ending.
• Hans Christian Andersen no Sekai (1971, The World of Hans Christian Andersen), Toei Animation's animated film based on Andersen's works.
• In the 1978 animated adaptation of "The Stingiest Man In Town", the character of Ebenezer Scrooge is seen passing by a caricature of the little match girl. Her first appearance during the musical number "The Stingiest Man in Town" shows Scrooge "buying" two packs of matches from her, only to pay her with a button from his coat and go on his way laughing at her expense, leaving her bewildered. Her second, and final, appearance in the special is in the musical number "Mankind Should Be My Business", it shows her shivering from the cold and a now-reformed Scrooge giving her his coat and a handful of gold coins.
• The Little Match Girl (2003), an animated short film by Junho Chung for Fine Cut: KCET's Festival of Student Film.
• "The Little Match Girl" (2005), ADV Films' adaptation released in Hello Kitty Animation Theater, Vol. 3.
• The Little Match Girl (2006), the last of four Walt Disney Animation Studios shorts originally intended to be part of a Fantasia (2006) compilation film, which project was canceled. This short was then developed as a stand-alone film and was nominated for the 2006 Academy Award for Best Animated Short, losing to The Danish Poet. This short was subsequently released as a special feature on the 2006 Platinum Edition DVD of The Little Mermaid (1989). In 2015, the short was released on the Walt Disney Animation Studios Short Films Collection Blu-ray Disc.
• "Allumette" (2016) by Penrose Studios Released as a free VR animated film for PS4 and PC.