Do assets without rental income streams appreciate relative to assets with rental income streams?
I believe he assumes that there is no arbitrage and also that there are no pricing bubbles. So two assets that have the same price today would have the same net present value.

Let $P_t$ denote the price of an asset in year $t$, $d_t$ the dividend (or rental income or cashflow) you get from said asset in year $t$ and let $r$ denote the interest rate (which I assume to be constant for simplicity's sake). Then the price of the asset today is
$$
P_1 = \frac{d_1}{1+r} + \frac{P_2}{1+r}.
$$
Using iteration
$$
P_1 = \sum_{t=1}^{n - 1} \frac{d_t}{(1+r)^t} + \frac{P_n}{(1+r)^{n-1}}.
$$
If you compare two assets with
$$
P_1^A = P_1^B
$$
where
$$
\forall t: \ d_t^A &gt; 0, \ d_t^B = 0,
$$
then or all $t&gt;1$ you will get:
$$
P_t^B &gt; P_t^A.
$$
This is somewhat paradoxical, as a there is no clear reason why $P_t^B$ should be positive if it never pays dividends. You could assume that it has not yet payed any dividends but will start doing so soon.

However I think Landsburg's main argument is that $d_t&gt;0$ holds for the house 
as well, not just the stock.