No, not easily possible. libtiff is in Arch Extra and is at 4.5.0-1 which includes libtiff.so.6. It was updated 2 weeks ago to the current version.
You are in some luck, that libjpeg.so.62 is in the Arch Community package libjpeg6-turbo, which you can install if you wish.
It’d be better to ask the package maintainer of the openmsx-catapult package if they can update for the current AUR packages. Or find a flatpack or appimage and run the app from there.