This unit. Hmmm.
The UL Listing on this unit looks legit, I'm looking at a photo of a unit "in the wild" with a proper File Number and yet a 3-prong socket. My research thoroughly checks out, they even applied for a California research grant. This is a small "mom & pop" US company that builds in California for Pete's sake - fully within reach of US regulatory talons. The UL listing can only be legit. Clearly, they found a way to make the NEMA 10 style connection less dangerous (?) in a way that fully satisfies UL.
So a first - no McKayla Maroney face from me, my tail is wagging. However their product doesn't make any sense for two EVs - Share2 does that, and does it better.
However, when UL approves an item, they approve paper instructions. These are important as they define the scope of testing, and they MUST be followed per NEC 110.3, and override any "more fun" multi-media instructions. Hiding them is a red flag. I'd like to see them.
It may not be necessary at all.
There is no limit to the number of receptacles on a 30A circuit. This has come up in the past here, and we have not been able to find any rule against this. So I do not see a problem with simply extending a legal, grounded 30A circuit to the garage and having a second receptacle there. Don't use the dryer and EV at once.
Note that an ungrounded circuit cannot be extended, unless you retrofit ground to the original location. (the GFCI solution below does not allow extension).
Those pesky ungrounded circuits and NEMA 10 receptacles.
NEMA 10 is a World War II era connector that does not provide safety ground. The madness of using this should be obvious. Even worse, on dryers, Code says to bootleg chassis ground to the neutral, on the logic that NEMA 10 sockets are rarely disturbed -- however, if they are disturbed and the neutral wire loses contact, this guarantees the chassis of the machine will be energized with 120V. Guarantees. The media reports these fatalities as a "miswired" socket, it was correctly wired and simply wore out. That shouldn't be possible, hence the ban.
Code never forces retrofit of things which were legal at the time of installation; this is called "grandfathering". However, such circuits cannot be modified or extended.
There are generally 3 solutions to a NEMA 10 outlet:
Open it up and discover there are separate neutral and ground wires in the box after all, or metal conduit rated to provide ground. Code required all dryer sockets to be wired this way as soon as the supply of ungrounded 3-wire was exhausted.
"Retrofit Ground" to that location using the now-liberal retrofit rules. A #10 ground can be run back to the panel obviously, or to the Grounding Electrode System (that bare wire going off to ground rods), or to any junction box with #10 or larger ground going back to the panel. (Grounds can be shared among circuits, since they only carry current during a fault).
Leave the circuit groundless, GFCI-protect the circuit at the breaker, fit a NEMA 14-30 receptacle with ground unconnected, and mark it "GFCI Protected / No Equipment Ground".
That is why I'm so keen on seeing the UL-approved instructions. Perhaps they approve 3-prong pass-thru to a dryer. If they do, that is that. (why would they approve that? Does the unit have GFCI?)
Proper in-wall wiring, though.
Routing an extension cord through a wall is not legal and cannot be done. Any thru-wall wiring must be done with proper in-wall wiring methods, e.g. NM cable and junction boxes in jurisdictions which allow NM cable (not Chicagoland).
If you are simply extending the circuit, this is straightforward standard wiring.
It is perfectly legal to use in-wall wiring methods in walls to connect an inlet to an outlet, that is otherwise isolated. For instance you could have a 10/3 NM cable in the walls between two junction boxes, with a NEMA 6-30 or 14-30 socket on one end, and a NEMA 6-30, L6-30, 14-30 or L14-30 inlet on the other end. Jay613 wisely pointed out in another discussion that the "L" twist-lock inlets may be more readily available than the non-"L". Then have an adapter cord that takes an L-x-30R (inline socket) to a "normal" 6-30P or 14-30P.