Should I get saftey testing if I want to sell on Amazon (game is rated 13+)

From publishers I've discussed this with over the years;

Regarding the UKCA and CE marks, if your product is clearly labeled and intended for those ages 14+ you should *not* have the UKAC/CE mark and the same goes for CPSIA/ASTM testing (for the US (but at age 13+).

HOWEVER, if your game looks, *in any way*, like it may be suitable for children under 14/13, simply saying it's for 13+/14+ may not be enough and you'll require testing, but only if it's disputed (for example, a cute looking game with chibi style characters who 'fight' one another with pillows could clearly be seen as a game suitable for children under 14).

ASTM Testing info:

https://www.herotime1.com/safety-test-for-board-game/

UKCA/CE Certification info:

https://www.herotime1.com/certification-for-board-game/
and
https://www.bigblue.co/blog/how-to-become-an-expert-in-board-game-custom...

Some mandatory requirements for marking for customs:

Age restrictions: minimum or maximum age of the user
Warnings must also be included in the product. It has to be preceded by the words “Warning” or “Warnings”.
Identification number: Toys made available in the EU market must have a type, batch, serial or model number or other element allowing for the identification of the toy.
Contact details: it shall indicate the name, registered trade name or trademark of the manufacturer and the address at which they can be contacted on the toy.
If the toy is marketed under another person’s name or trademark, that person will be considered as the manufacturer.

Note that these requirements apply for any game even if its target audience is above 14.

As for Amazon, I don't know about their requirements. My limited experience trying to sell via Amazon was non-productive and they didn't require much at all (at the time, 2018).