Embossed vs. printed
Embossed credit cards are credit cards that have raised numbers. The purpose of the raised numbers is to allow the card to be used with carbon papers in a "zip-zap" offline machine. Printed cards without the raised numbers cannot be used with this machine. Functionally, this is the only difference between the two types of cards. Until relatively recently, just about every credit card had embossed numbers.
The carbon paper zip-zap devices are essentially obsolete. It is extremely easy for merchants to get online (you can process credit cards by smart phone today), and the carbon papers presented a security risk. I haven't seen one of these machines in years.
It is more expensive to manufacture an embossed card than it is to make a printed card. As a result, most gift/prepaid cards were printed to keep costs down.
The trend, however, is for all credit, debit, and gift cards to be printed. I have already received credit and debit cards with printed numbers.
Gift/Prepaid/Debit vs. Credit cards
I've looked at the advertising for the VIABUY card you are looking at. The issue they are talking about is that certain merchants might be reluctant to accept prepaid cards. Hotels are a big example of this: when they run your credit card at check-in, they might get approval for one night, but they want to be reasonably sure that if you stay longer or cause damage, they will be able to charge more. With a real credit card, they are more likely to be able to get more money if needed than with a prepaid, gift, or debit card. I've seen signs on hotel check-in desks asking customers not to use debit cards.
This particular card is designed to look like a credit card, in order to not give away the fact that it is a prepaid card. It doesn't say "prepaid" or "debit" on it, it is customized with your real name, and it has embossed numbers. But as I mentioned above, the embossed numbers on any card today are essentially cosmetic.
Offline transactions
Offline credit card transactions used to be quite common, but are rare today. You might occasionally see them if you buy something at a home sales party: the sales person will write your card number down on the order form and enter it online when she gets home. If the transaction gets rejected at that time, the sales person will simply cancel the sale and call you.
Credit card issuers used to guarantee offline transactions up to a certain dollar amount because they were so common. I don't think they do this anymore.
To answer your question, I don't think you would have a problem using this card in an offline transaction, on the rare occasion that you find yourself in that situation.