So ,i tried yout code, and it did work, but i did see some syntax issues.
In most cases if you make one or two small mistakes in HTML, the browser 'fixes' it for you.
The 'mistakes' i saw are:
1. The button doesnt termintate. For each HTML element, it needs to terminate, ie. open, and close.
There are 2 ways to do this.
<tag id="tag1">somestuff</tag> (open and close )
<tag id="tag2" /> (self closing)
You seem to close the FORM element with a "</FORM>" at the bottom, but you never self closed the "INPUT" element.
2. It might not be the cause, but it should be addressed, is that you dont have any HTML tags either.
All html documents need to start and end with <html>...</html>
And should also contain a header, and body elements.
Here is your code, with my small modifications:
VALUE="click here to add a game"
onClick="parent.location='mailto:firstname.lastname@example.org?subject=I would like to add a game to the website'" />
I hope this helps
PS, For more info, try using the W3Schools website: http://www.w3schools.com/html/