In laymen’s terms what it says is the President of the Senate (Vice President Mike Pence] in the presence of the Senate and House of Representatives opens all of the envelopes containing the Electoral votes and then the votes are counted.
The Amendment does not say who is to count the votes. The language appears to suggest that the vice present both opens the votes and counts the votes.
If that is the case, Vice President Pence could conceivably, on his own judgement, say that fraud was rampant in the states in question and disqualify their votes which would mean that the House would elect the president and, even as the Democrats have a numbers advantage in the House, Republicans would have the advantage in this case.
Each state would be given one vote for president, not each member, and the Republicans have a significant edge on that number.
Will Vice President Pence do this? There is no way to know until that day, but it makes that normally mundane process something to watch.