Can I SAFELY install a Grounded Dishwasher in a mid 1950's home which was wired with a 2 wire UNGROUNDED circuit?
Looks like cheese junk from a brand no one's heard of.   You certainly shouldn't use random stuff that fell off a truck in Shenzhen for life safety. 

It's also too expensive for what it is.  Cheaper would be a GFCI breaker from top makers like Eaton, GE, Siemens, etc.  Cheaper still would be a GFCI receptacle from a decent maker. 

In any case, the device has a 5-15 plug, which means it's not listed to use on an ungrounded receptacle, if it's listed at all, which I doubt.    Which means either a) it won't plug into your receptacle; b) you have a 5-15 receptacle that is illegally installed with no ground, c) you have a GFCI receptacle legally installed without ground, or d) you have a 5-15 receptacle that does have a ground after all.  

I would do option C and install your own GFCI receptacle or breaker, and call it done. 

A GFCI is adequate for life safety, as it will stop electrocutions.  Some equipment needs proper earthing for reasons not related to life safety, e.g. radios or recording studio equipment, a GFCI will not suffice for them.