The fitting your link leads to is likely NOT the fitting you need.
Your dryer has a male 3/8" NPT (commonly referred to as 3/8" pipe thread) inlet to which an adapter has been attached. The adapter changes the male 3/8" NPT to 3/8" male flare thread to fit a smaller flex supply tube than the one in your second picture. NOTE- NPT (pipe thread) and flare thread are distinctly and deliberately not compatible with each other, hence the use of an adapter.
To connect your flexible supply tube to the dryer you would need to remove the existing adapter from your dryer inlet and install a fitting that will fit your flex line. I suspect that the connection nuts on your flex line have 1/2" flare threads (I say "suspect" because your picture does not show the inside of the nut; disregard the size stamped on the nut because that is a reference to the nominal inside diameter of the flex tube itself, not the thread in the connector nut).
You will need this adapter: 3/8" FIP (female iron pipe; or "pipe thread") x 1/2" male flare. It will look like this:
NOTE- always ensure that your flex supply line is rated for use with the fuel supply (in your case propane/LPG). Also, the manufacturers of those flex supply lines generally consider them a "one time use" product and do not recommend re-using them.