A relative aged 66 has no assets other than his house which is wholly owned and worth £150,000. I plan to gift him £500 per month.  If he gifts me a share of the house, perhaps every 2 years, to compensate me in full - does this constitute an Equity Release Scheme which would impact his Pension Credit, etc?

Any buyer and seller can claim that they are 'gifting' to each other, and that nothing commercial has taken place, but the reality is that a sale has happened.

It sounds to me that this is applicable to your scenario, and that there is either a sale here, or an Equity Release Scheme. Since calculation of Pension Credit takes into account the amount of capital the individual has over £10,000, it could impact on his entitlement to Pension Credit.