#!/bin/sh
x=( foo bar "Hello World" )
for word in "${x[@]}"
do
  touch "$word.dat"
done

Consider switching to a shell that does support arrays, such as bash or ksh, by changing the shebang.

Alternatively, if you only need a single array at a time, you may be able to rewrite to use the positional parameters:

set -- foo bar "Hello World"
for word in "$@"
do
  touch "$word.dat"
done

or strings with carefully chosen delimiters:

x='foo
bar
Hello World
'

printf '%s' "$x" |
  while IFS='' read -r word
  do
    touch "$word.dat"
  done

Arrays are specific to Bash and Ksh, but you are using them in a script declared to run with sh or dash. These shells do not support arrays at all. You should either switch to Bash/Ksh, or rewrite the script to not use arrays.

There are no great replacements, especially not that can be mechanically applied, but using the positional parameters or a delimited string works in many cases, as shown in the examples.

None.

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