Can I use an adapter to connect a welder to a dryer outlet?

Yes that looks like an appropriate adapter for the job.

It is a metal working convention to put the 6-50 plug on welders, plasma cutters, and the like even when they require nowhere near 50 amps to operate. I guess it's analogous to every kind of small appliance (table lamps, alarm clocks, etc) using a 5-15 plug even though they'll draw nowhere near 15 amps. As the 5-15 socket is just the standard around the house; so also the 6-50 socket is the standard around the metal shop.

These are not legal and cannot obtain a UL listing; therefore reputable home stores won't sell them. They are only offered via shady sales channels like AliExpress, BangGood, eBay or Amazon Marketplace, which is an eBay-like flea market folded into Amazon listings.

Some are cheap Chinese and others are built out of UL-listed parts by handymen in their basement.

Another option for you is simply change the welder cord to NEMA 14-30. Dryer cords are readily available that should suffice.