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.