Does a non-EEA spouse, travelling to the UK without their EEA national spouse, require a visa?

No, your residence card and passport are not sufficient. Neither is an EEA family permit, which anyway you won't be granted because you are traveling without your spouse. You need a Standard Visitor visa.

Note the eligibility requirements, which include (emphasis added) that

The EEA citizen you’re joining must either:

• be in the UK already
• be travelling with you to the UK within 6 months of the date of your application

Because you do not qualify for an EEA family permit for this trip, you should apply for a Standard Visitor visa instead.

Your Article 10 residence card only qualifies you for freedom of movement when you travel with your EEA family member. Directive 2004/38/EC provides for visa-free travel, for example, for holders of a residence card, but the UK has interpreted this as applying only when visiting the UK with the EEA family member. Their page on the subject says

in order to be admitted to the UK you will need to demonstrate that you have a right of admission under EU law. Without evidence that you have a right of admission, you will not be allowed to enter to the UK on the basis of your residence card.

It continues (emphasis added):

if you are not travelling with your EEA national family member, you will also need to show:

• evidence that your EEA national family member is in the UK, and
• evidence that they have a right of residence in the UK because:
  1. they have been in the UK for less than three months, or
  2. they are in the UK as a worker, self-employed person, self-sufficient person or student, or
  3. they have acquired a right of permanent residence in the UK under EU law.