The code within that input field is custom code, not controlled by Hype, but likely inserted within the inner HTML of a rectangle. It is this:
<input type="text" id="StatusER_txt" onclick="SelectAll('StatusER_txt');" value="01 item" size="14" style="
border: 0px solid #D8DDE4;">
If you add line-height:1; (which will multiple the font-size by 1) your
line-height will become
18px. This will likely standardize the line-height across all browsers.
Forms are notorious in how different browser treat them. This is also why there are so many 'reset' CSS libraries, which aim to standardize browser quirks. Here's a popular one: http://cssreset.com/scripts/eric-meyer-reset-css/
Adding that reset CSS to the head of your document might also help out.
A bit more background:
I used Safari developer tools (while connected to my iPhone) to see what the line-height being computed was for that:
Line height for that element magically became '24px' because the line-height had not been set, and 24px seemed right because the height of the parent element for the input is 24px. That's Safari for ya.