Araya 27 1 1/4 rim and tire, max pressure
Don't worry about damage to the rim from air pressure in the tire if you inflate the tire to the recommended inflation range.

To say it a different way:

If you inflate your tire somewhere between 73 and 90 psi as labeled on the tire your rim will be fine. The pressure won't damage your rim. The steel or aluminum the rim is made of is much stronger than the material the tire is made of - assuming the rim is not damaged (extensive corrosion etc.)