Did somebody mention rivers? :-)
Nice start, Dysterkvist, and I totally approve of interpreting the rules to suit what you want to map. I have done that multiple times... one just has to figure interpretation of the rules is also the perogative of each and every voter. In any case - already looking good, and I look forward to seeing it develop.
As far as internal dead-end lakes... nothing wrong with them per se. If you read & digest the Most Excellent Redrobes tutorial
How To Get Your Rivers In The Right Place you may get a better feel for just what would cause such topography & hydrography. If there's scant rainfall, evaporation can keep pace with inflow. You do get some specific characteristics -- those three dead-end lakes are going to be mighty salty! If there's a lot of rainfall though, over centuries the water level would rise, making for a huge internal lake, and eventually whatever point is lowest on the surrounding divide would be reached by rising waters, and an outlet river would form. The point it drains at would gradually wear down by erosion, lowering the large inland sea bit by bit, with an outlet that got more and more canyon-like. If the rim was geologically fragile that erosion could happen fast - either geologically fast or actually fast on a stopwatch, making for a catastrophic flood. Which would be an awesome story element, and an interesting bit of worldbuilding.
But what you show more matches the "must not be enough river flow to exceed evaporation" case.
If you want your continent to look more "normal" (whatever THAT is :-) ) you could draw outlets to the sea to one, two, or all of those. If you want the interior of your continent to be dry, with Dead Sea/ Salton Sea/ Great Salt Lake kind of environs -- you're there.