"The mark of the beast is the papal sabbath"
{Signs of the Times, November 8, 1899}
The children of Israel have come to worship God not only on the Sabbath Day, but also on other days of the week. For example: Nehemiah 8:6 & 9:3 outlines a situation where the whole of Israel came to worship God on the 1st day and the 24th day of the month: "...upon the first day of the seventh month...they bowed their heads, and worshipped the LORD with their faces to the ground." and "Now in the twenty and fourth day of this month...and another fourth part they confessed, and worshipped the LORD their God."
Suppose the 1st day of the month happened on the seventh-day Sabbath, then the 24th day of the same month will not be on the seventh-day Sabbath. Or vise versa.
In the gospel account, many people worshipped Jesus immediately after they received healing. And many of these instances occurred outside of the seventh-day Sabbath.
Hence, we can conclude, worshipping on a Sunday or any other day in itself is not the Mark of the Beast.
Mark of the Beast signifies the defiance of God's authority to establish its own authority.
For it is written: "for the seventh day is the sabbath of the LORD thy God." Exodus 20:10
Satan, seeking to DEFY God's authority and ESTABLISH his own authority says to the Christian world: "the seventh day IS NOT the sabbath! and the first day IS the sabbath."
DEFY = IS NOT
ESTABLISH = IS
Therefore, the mark of Satan's authority is the papal sabbath. Thus, to keep (recognize, remember, acknowledge, pay homage to, etc...) the Sunday or the first day as the sabbath of the Lord in defiance to the keeping of the seventh-day sabbath is to receive the Mark of the Beast.