How can non index shifters be limited to a specific range of gears? Searching on eBay, I find shimano SL-MY34s. Description says that they should only be used with 5/6/7 gears. What limits them to this range?
The main limiting factor is probably total cable pull. Moving between the largest and smallest gears requires pulling a certain amount of cable, which is determined by the design of the derailleur. It's possible that Shimano's 8-and-more-speed derailleurs require more cable pull than the lever can manage.

Also, more gears means a smaller movement of the lever to change gear. With five gears, the lever moves about 36&deg; per gear but with, say, ten gears, there would have to be only 18&deg; of lever movement per gear. At some point, the lever movement will become too small to perform accurately.