It's good that they are doing some customer identification, but, from a US legal perspective, that doesn't cut it. If Bitstamp is a foreign MSB servicing US customers, then it is subject to the so-called Foreign MSB Rule, requiring, at minimum, FinCEN registration. It also must register in those states that have adopted extraterritorial jurisdiction, like NY.
Regarding Fincen rules, they would still have to have some sort of US presence. Does bitstamp even have a bank account in the US?
By 'Foreign MSB Rule' I assume you mean the 2011 amendments to 31 CFR 1010.100(ff), which replaced
Each agent, agency, branch, or office within the United States of any person doing business, whether or not on a regular basis or as an organized business concern, in one or more of the capacities listed in paragraphs (ff)(1) through (ff)(6) of this section.
with
A person wherever located doing business , whether or not on a regular basis or as an organized or licensed business concern, wholly or in substantial part within the United States, in one or more of the capacities listed in paragraphs (ff)(1) through (ff)(7) of this section. This includes but is not limited to maintenance of any agent, agency, branch, or office within the United States.
However, to be considered a 'financial institution' under 31 CFR 1010.100(t), they would have to have an "agent, agency, branch, or office within the United States".
The state law issues are more messy. The scienter requirement of 18 USC § 1960 only applies to knowingly operating a money transmitting business and not whether it was required to be licensed under state law.
If a New York resident wires money to Bitstamp, is Bitstamp really operating a money transmitting business in New York? They weren't the ones who sent the money from NY.
What a mess.