The poorer/richer argument only makes sense in the context of a specific consumption basket. If your main goal in life is to buy as many bananas as you can (for example), then you would measure the house appreciation in bananas. Can you get more bananas for your house now (at $1M - 250k) than you could when you got it? Then you're "richer", otherwise you're not.
Usually we use CPI as a proxy for it. However, most people when evaluating houses ignore the implied rent paid; owning a house means not having to pay rent - and that has a specific price on it, depending on your local rental market. So in a relative sense, you owning that house makes you richer relative to the people that did not own a house (who did not get the same nominal appreciation at all and are much worse off), and leaves you at the same place with other people owning the house. You're unlikely to be worse off (on a relative standing) than if you hadn't gotten the house. So I'm not sure richer/poorer makes sense without considering the alternatives (i.e. renting & investing)
Usually we use CPI as a proxy for it. However, most people when evaluating houses ignore the implied rent paid; owning a house means not having to pay rent - and that has a specific price on it, depending on your local rental market. So in a relative sense, you owning that house makes you richer relative to the people that did not own a house (who did not get the same nominal appreciation at all and are much worse off), and leaves you at the same place with other people owning the house. You're unlikely to be worse off (on a relative standing) than if you hadn't gotten the house. So I'm not sure richer/poorer makes sense without considering the alternatives (i.e. renting & investing)