How are you so sure that there aren't any M&Ts in the original table construction? The table looks square and tight and gives no reason to suggest that M&Ts weren't used. If I was constructing such a rustic table that's how I'd build it. I would never judge any table by the top as if they're old then very often they may have been damaged or wormed and someone replaced it with available boards however in this case, looking at it's prominent position in the room it's displayed in, I'd think it's very likely to have been made that way deliberately.
The matching bench seating also suggests that it was deliberately made that way too.
Sorry, I know this may irk some of the crafts people on here but some people do make tables and the likes that they want to actually look that way! Rustic to some people is just as good to them as finely crafted furniture is to other people. Rustic can look very good in the correct settings so never discount it completely.
Heaven forbid some people even like furniture from Ikea...there's just no accounting for taste, thank goodness or the world would be a very boring place.
Post #66 about nails it for me, that's how I'd suggest the OP approached it if their skills are sufficient and I'd maybe add a couple of dowels just to keep the joints in place as they would in centuries gone by. Three of my smaller tables which are used daily I've constructed that way, the only difference is that they are French polished rather than rustic.
If the OP hasn't got the skills and not enough time to learn them the I'm sure YouTube has plenty of ways of constructing tables like that with wood or metal brackets.