A question about interpreting a supply's spec
Does it mean the max output current will decrease linearly with
temperature but the voltage will remain the same between 50 and 70
degrees?

Yes, the voltage will remain constant up to 70°C but the availability of current to the load will linearly reduce between 50°C and 70°C for units producing higher than a 5 volt or 12 volt output.

What is meant by Load(%) here?

It is a way of indicating the proportion of full load current without talking about amps. It doesn't mention amps because each power supply will have a different nominal full load current and showing all three power supply types on the same graph would appear confusing.

Does it mean if the nominal current is given as 10A for a model. It
will be like 5A at 60C?

See the graph and redlines below: -

A 15 volt power supply will be capable of supplying about 76% full load current at 60°C whereas a 5 volt output device is only capable of supplying 66% full load current at 60°C.