For a domestic-international connection such as this, you'll simply have to get yourself to the next gate. No other procedures or security checks are involved. ORD is a large airport, but 1:32 should be plenty of time unless your inbound flight is delayed. For example, today's UA1087 arrived at gate C31, while today's UA895 left from gate C18, just down the hall of the same concourse. That may not always be the case, but the gates will be connected without having to go through security, possibly through the funky tunnel.
If there are delays and you do not make the Hong Kong flight, United will book you onto another flight free of charge, though you may be responsible for expenses in the meantime (such as a hotel room), particularly if the delay is caused by weather or another factor outside the airline's control. United only has the one daily flight from Chicago to Hong Kong, so if you miss it, an alternate routing could mean a significant delay.
It's absolutely doable if there aren't delays. Personally, I like to leave a longer buffer before connecting to infrequent long-haul flights, and it looks like there are a number of IND-ORD flights to choose from, so I might choose an earlier flight and a longer layover, but it comes down to your preference and tolerance for risk.