Is a holding company classed as an investment company?

Technically, Yes.

In order for a holding company to hold any form of controlling equity in another entity, it would need to do so by way of equity capital, not debt capital.

If the relationship between 'holding company' (A) and the entity held (B) was formed by way of A introducing debt capital (any form of loan instrument) to B, that relationship would be deemed to be one of a debtor / creditor relationship, thereby not qualifying A to have equity ownership in B unless it arises out of a default by B.

There are numerous ways an entity can end up forming part of the assets of a holding company - by example: 1/ An arm's-length transaction (acquisition of the shares); 2/ A cession or pledge of shares in securitatum debiti that were exercised; 3/ A merger;

Thus, if the term 'investment' implies a conscious decision by A to acquire an interest in B, then that is an investment. However, if A acquired its' interest in B by default, it is no less a conscious decision, as the provisions for default were clearly set out in the loan instrument agreement - i.e. a pre-supposition that in the event of default, one of the remedies for A would be that the shares of B would be held as security by A as an asset to be held or realised in judgement execution. The results are similar in pre-meditation.