[Ken Case]

You're almost there! You just need to pull out the id of the first item in the array, then use that id to look up the project. Like this:

display dialog "Enter Project to Find" buttons {"Cancel", "Find"} default button 2 default answer "" with title "Project Find"
if button returned of result is "find" then
	set ProjectString to text returned of result
	tell application "OmniFocus"
		set MyDoc to default document
		tell MyDoc
			set MyProjectArray to complete ProjectString as project maximum matches 1
			set MyProjectID to id of first item of MyProjectArray
			set ThisProject to project id MyProjectID
			set newW to make document window with properties {focus:{ThisProject}, selected view mode identifier:"project", search term:""}
		end tell
	end tell
end if