Coolwave, there is a way to put the games in posts, but it is not recommended. Not even if you know enough about HTML to figure out all the tags you must allow.
As the tutorial you linked to says:
Note: We recommend that only users with an understanding of HTML use the "post" option. As enabling and adding tags to the allowed list on your forum, can leave your forum open to members posting malicious scripts.
With all the HTML tags needed for embedded game scripts, and with HTML enabled in posts, the members can intentionally post malicious scripts, making a mess of the forum, and/or "freeze" many a member's computer...
And they can also unwittingly post faulty code -- a copy and paste mistake, or quite simply a typo -- that messes up the forum.
I would follow your own advice, and put one or a couple of games in forum descriptions.
If you want, you can make the game forums visible for registered members only, to get a neater and more fast loading page for visitors (and to log on from).
Forum Admin >> Permissions
Choose forum from the drop-down menu, click Look up Forum
Simple mode, and a new drop-down menu, where you choose
Registered [hidden] and click submit.
FoxLeonard