What does the cointegration coefficient represent in pairs trading when cointegrating log stock prices?

In Pairs Trading by Vidyamurthy, on page 83 (and throughout the book), the author describes an elementary example of trading with log prices. The long run equilibrium of the basic portfolio is given by

$$\log(p_t^A) - \gamma \log(p_t^B) = \mu$$

where $p_t^A$ and $p_t^B$ represent the prices of stocks $A$ and $B$ at time $t$, respectively, and $\gamma$ is the cointegration coefficient. When using these log prices, Vidyamurthy uses the cointegration coefficient ($\gamma$) to indicate the ratio of shares to hold rather than market values of positions (as stated should be the case here, for example).

My questions are:

What is the correct practical interpretation of $\gamma$ when cointegrating log prices, should it represent the ratio of shares or the ratio of market values? If the latter, why does Vidyamurthy use the former interpretation throughout his book? Could both be valid?

Here is the example from the book: • From my experience, I'd say you should always compare stocks using their market values, because assets may have different delta, so is the volatility of the PnL equity. For example, buy ES futures @3000 and sell SPY stock @300. You think that multiplying SPY by 10 would be enough, e.g. 300 x 10 = 3000 = SPY = ES and portfolio is market neutral. Meanwhile, when price goes against you, you'll notice that each tick step of ES loses 50 USD and SPY compensates only 10 USD, because ES delta = 50 and SPY delta = 1. Market value will take delta into account. Sep 5 '20 at 4:37