Why can per share earnings growth only keep up with GDP growth, if no new shares are issued?
The question is really about industry jargon, not economics.


  Wouldn't company B's faster rate of share price increase increase my
  portfolio's value?


What he's referring to is that, at the moment company B went public, shifting your portfolio to company B stocks is simply a re-balancing of your portfolio. There is no profit from re-balancing.

(Of course, once a stock is in your portfolio, there is capital gain if stock price increases, vice versa.) 

On the other hand, in the scenario where equity value increases at the moment of IPO, the value of the company increases, which contributes to increase in overall market value (what he calls "GDP growth" and "economic impact").
The difference in value is captured by investors who holds private equity prior to public listing (e.g. venture capital firms).

Each time this occurs, there is capital gain in the economy that's not captured by investor in public markets, simply because they are late to the bandwagon.
This is what he calls "slippage". He claims "over time, the effect of this slippage has been meaningful", which implies the gains of public market investors lag gains
of private equity investors.

(If one compares the historical returns of the public market---e.g. that of stock indices---and the average VC firm, the latter is probably higher. However, it's not clear whether this is still the case after adjusting for  risk. The risk profiles are very different. The typical VC portfolio may have 30 companies, with one eventually turning a profit.)

A rephrasing of the quoted statement might be:

"...per share earnings growth [for investors in public markets] can only keep up with GDP [(market cap)] growth, if no new shares are issued [i.e. no new public listings occur]..."