Yes..

The accepted answer correctly quotes the U.S. Customs and Border Patrol advice, however nowhere in this advice does it point out that CBP does not consider trains to be land. What they actually mean is arriving by road.

I know this from first-hand experience having departed for the U.S. by Amtrak starting in Vancouver. There I was firmly chastised for not having completed an ESTA. Only when one of my friends questioned this was it understood that we had followed the instructions as we understood them, but our understanding was wrong.

The Amtrak website claims:

Amtrak Cascades trains do not fall under the U.S. CBP “Land Border Crossing” definition.

 

Travelers crossing from Canada into the U.S. on Amtrak Cascades trains AND are NOT U.S. or Canadian citizens nor have a valid visa, MUST have an approved ESTA, otherwise a paper form CBP I-94 will be required.

Getting a paper form I-94 is possible but it means delays at best, according to the CBP:

If a traveler would like a paper Form I-94, one can be requested during the inspection process. All requests will be accommodated in a secondary setting.

Yes..

The accepted answer correctly quotes the U.S. Customs and Border Patrol advice, however nowhere in this advice does it point out that CBP does not consider trains to be land. What they actually mean is arriving by road.

I know this from first-hand experience having departed for the U.S. by Amtrak starting in Vancouver. There I was firmly chastised for not having completed an ESTA. Only when one of my friends questioned this was it understood that we had followed the instructions as we understood them, but our understanding was wrong.

The Amtrak website claims:

Amtrak Cascades trains do not fall under the U.S. CBP “Land Border Crossing” definition.

Travelers crossing from Canada into the U.S. on Amtrak Cascades trains AND are NOT U.S. or Canadian citizens nor have a valid visa, MUST have an approved ESTA, otherwise a paper form CBP I-94 will be required.

Getting a paper form I-94 is possible but it means delays at best, according to the CBP:

If a traveler would like a paper Form I-94, one can be requested during the inspection process. All requests will be accommodated in a secondary setting.

Yes..

The accepted answer correctly quotes the U.S. Customs and Border Patrol advice, however nowhere in this advice does it point out that CBP does not consider trains to be land. What they actually mean is arriving by road.

I know this from first-hand experience having departed for the U.S. by Amtrak starting in Vancouver. There I was firmly chastised for not having completed an ESTA. Only when one of my friends questioned this was it understood that we had followed the instructions as we understood them, but our understanding was wrong.

Yes..

The accepted answer correctly quotes the U.S. Customs and Border Patrol advice, however nowhere in this advice does it point out that CBP does not consider trains to be land. What they actually mean is arriving by road.

I know this from first-hand experience having departed for the U.S. by Amtrak starting in Vancouver. There I was firmly chastised for not having completed an ESTA. Only when one of my friends questioned this was it understood that we had followed the instructions as we understood them, but our understanding was wrong.

The Amtrak website claims:

Amtrak Cascades trains do not fall under the U.S. CBP “Land Border Crossing” definition.

Travelers crossing from Canada into the U.S. on Amtrak Cascades trains AND are NOT U.S. or Canadian citizens nor have a valid visa, MUST have an approved ESTA, otherwise a paper form CBP I-94 will be required.

Getting a paper form I-94 is possible but it means delays at best, according to the CBP:

If a traveler would like a paper Form I-94, one can be requested during the inspection process. All requests will be accommodated in a secondary setting.