I think, that to be a veteran game show host, you need to host more then one game show for one thing, and secondly, at least 2 of them have to have good runs. By good runs, I mean at least 4 years or more. Granted there are a few exceptions to this. Art Fleming, is one. Since he only hosted Jeopardy to my knowledge(though he did host more then one version) and Pat Sajak is also one, unless you count the daytime and nighttime versions of Wheel of Fortune separate.