In that case I assume if a person is interested in such an investment he would have to privately contact the site with an offer?!
No, you don't need to contact those sites privately as they have a dedicated page for bankroll investment. For example, bustadice
https://bustadice.com/investThe site that was mentioned in the OP doesn't highlight which gambling sites are currently in need of investments.
It does. The third column ("Investing") tells you whether you can invest in their bankroll or not.
No. There are lots of sites already with this feature but no one till now got success or make big profits out from investing in a site's bankroll.
Most of the sites that accept investments aren't making big profits but a few ones do. Again, look at the total profit history of bustadice. On this date last year their total profit was on
BTC898 vs today
BTC1276. That's roughly more than 35% return over a year, which is huge.