I am installing a YS 160 engine on an airplane that had an OS engine. The airplane has two rubber strips on each wood engine beam which has signs of being compressed from previous installation. Also, when I install the new YS engine the rubber strips compress and change the angle of incidence of the engine (down and up trust). I have never seen this type of mount before. Am I missing something from this mount? Thank you in advance for your help.

Not sure exactly which mounts you have in there, but it does appear you are missing some parts.
Here is a pic of the Dave Brown mounts for a 4 stroke. It is available at central hobbies.
I have a plane that had a YS 140 mounted on wood rails with this style of mount, but it kept breaking the mounts due to rotational stresses. It's not so much the vibration but the rotational effect the YS engines exert when they shake that these type of mounts are not designed to handle.