Are animated GIFs Recognised as videos or images in court?

They could be admitted into evidence if they are otherwise admissible as evidence.

Typically, the main issues would be authentication, foundation and relevance, i.e. that these videos are accurate evidence of something relevant to the lawsuit.

Conceivably, depending upon the content and the purpose for which they are admitted, other rules of evidence could be implicated such as hearsay, character evidence limitations, and rules regarding when deposition testimony is admissible.

It is also conceivable that they could be admissible as "demonstrative evidence" such as an animation used by an accident reconstruction expert to explain how an accident probably happened.

The medium itself isn't really material. Courts routinely allow AV evidence to be admitted, although it is sometimes necessary to make arrangements for the logistical details involved in presenting it at trial with the court clerk or in a pre-trial conference.

Sometimes the court itself can only handle certain file formats, and if it is unable to use your file format, you may need to bring your own equipment to display those files to the trier of fact.

They are both “documents” under most rules of evidence

Basically, there are only two sorts of evidence:

1. Testimony. What a witness says to the court. Although, in practice a lot of testimony is said out of court and given in writing but it’s still testimony.
2. Documentary. Everything else.