Yep, sounds like you have it well in hand after that first step. I think cyclometallations usually do require free coordination sites, but I suppose how many and in what arrangement will be dependent on what metal is doing the chemistry.
I don't have a great reference that talks about cyclometallation, but there is a section on page 106 of Transition Metals in the Synthesis of Complex Organic Molecules by Hegedus.
I should say that the mechanism is probably a little bit different when other metals are used. For example, if Co2(CO)12 is the metal then the metals will form a complex with the alkyne initially and then undergo more typical migratory insertion steps.