The answer to this question is provided by the European Commission.

Article 2(1)(k) DORA provides that it applies to managers of alternative investment funds. Under Article 3(44) DORA which refers to 4(1)(b) of Directive 2011/61/EU managers of alternative investment funds covered under DORA are defined as ‘legal persons whose regular business is managing one or more AIFs’
However, Article 2(3)(a) DORA specifies that the Regulation does not apply to AIFMs referred to in Article 3(2) of Directive 2011/61/EU.
Article 3(2) of Directive 2011/61/EU exempts from the scope of that directive certain AIFMs, whose assets under management fall bellow certain thresholds ("sub-threshold" AIFMs).
Since DORA explicitly refers to the second paragraph of Article 3 of Directive 2011/61/EU only, it cannot be inferred that AIFMs other than those referred to under Article 3(2) AIFMD are excluded from the scope of application of DORA. As a result, DORA applies to AIFMs as defined under Article 3(44) with the exemption of sub-threshold AIFMs referred to in Article 3(2) of Directive 2011/61/EU, which are excluded from the scope of application of DORA.

Disclaimer provided by the European Commission:

The answers clarify provisions already contained in the applicable legislation. They do not extend in any way the rights and obligations deriving from such legislation nor do they introduce any additional requirements for the concerned operators and competent authorities. The answers are merely intended to assist natural or legal persons, including competent authorities and Union institutions and bodies in clarifying the application or implementation of the relevant legal provisions. Only the Court of Justice of the European Union is competent to authoritatively interpret Union law. The views expressed in the internal Commission Decision cannot prejudge the position that the European Commission might take before the Union and national courts.