Can my domain be claimed by the owner of the other domain for any legally valid reason?

Technically, they are two entirely different legally-registered domain names for two different businesses in two different countries. However, given the international nature of the Internet, it is possible that there will be some confusion for customers. You will want to stress in all your advertising and publicity your full domain name.

I would not be so worried about their domain as their trademarks. If either XYZ or abc is a trademark of someone else, and you are selling similar goods or XYZ or abc is a famous mark, then yes you should worry. They could get the domain name away from you and could sue for damages.

Domains can be taken over by another party - under limited circumstances. Typically the second domain is a sham - not a legitimate business - and the owner offers to sell the domain to the first party for an outrageous sum of money. Such bad faith tactics can lead to the loss of the second domain to the first party - under the uniform domain name dispute resolution rules of ICANN. However - two legitimate businesses - each operating under similar domains - can co-exist without problems.

Your domain name is different. There generally shaould be no proble. However depending on who has what trademarked, it may not be that simple. Please search further.