I think people are reading your title wrong, and not looking at your adapter link.
It sounds like you simply want to use your 120v 13a OEM Leaf EVSE(not upgraded one) on your 240v dryer circuit and while it's possible, I'm not sure it's safe nor really needed if you have a decent 120v outlet nearby. The reason it might not be safe is the 10-30 outlet doesn't have a dedicated ground, just a neutral and 2 hots. True the neutral generally bonds with the ground back at the breaker/fuse box, but the ground is really supposed to have it's own path. Another reason it's kind of unsafe is you'd have a 30 or 40a breaker hooked to a device expecting a 15 or 20a breaker, IOW your EVSE and wiring past the outlet won't really be protected by the breaker.
So to answer your question, yes that outlet adapter should work to get a 120v circuit with tons of capacity, you really don't need it for a 13a 120v EVSE, again assuming you have a good 120v outlet nearby.
Now what I'd do would be to purchase 16a or better yet 24a(or higher amp that would let you set the maximum current) 240v EVSE and make use of your high current 240v outlet. 16a 240v EVSEs can be had for as little as $200 with 24a+ ones probably between $300-$400 that would charge your '19 Leaf at near it's maximum 27.5a(6600kwh) speed.
16a 120v/240v portable EVSE with correct 10-30 plug, the one you linked:https://www.amazon.com/Zencar-Portable- ... ive&sr=1-3
Very interesting 26a 240v EVSE(2a more than what the maximum should be for a regular 10-30 outlet with 10g wiring and 30a breaker, you gotta love the Chinese for pushing the limits
) but at $329 and with your correct plug, might be just the ticket for you. Note you can't adjust the current lower than 26a but from what you've said, 26a should be just fine and darn near the maximum 27.5a of your Leaf, so that's good. Note 10g wiring is generally rated for a full 30a as well as your 10-30 outlet, the breaker is what needs to be de-rated to 24a and since you already have a 40a breaker, this EVSE should be really ideal for you.https://www.amazon.com/MUSTART-Portable ... ive&sr=1-4