Let's look at a simpler example to show the problem. We'll create a Delaunyey mesh from some random points, and generate a RegionBoundary from that.

In version 10.4:

SeedRandom[4];
mr1 = DelaunayMesh[RandomReal[1, {15, 2}]];
mr2 = RegionBoundary[mr1];
Show[mr1, HighlightMesh[mr2, 1], 
 ListLinePlot[MeshCoordinates@mr2, 
  PlotStyle -> Directive[Thick, Red]]]

compared with version 10.3.1 (or any previous version 10.x)

Let's look at the InputForm for this in 10.4,

mr2 // InputForm


MeshRegion[{.....}, {Line[{{2, 6}, {1, 2}, {4, 1}, {3, 5}, {6, 3}, {5, 4}}]}]

versus for 10.3,

MeshRegion[{.....}, {Line[{{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6,1}}]}]

How to get around this? Create a BoundaryMeshRegion and extract the polygon points from that (the points of a polygon must be in the right order or it's nonsense). The following gives identical results in 10.3 and 10.4

SeedRandom[4];
mr1 = DelaunayMesh[RandomReal[1, {15, 2}]];
mr2 = BoundaryDiscretizeRegion[mr1];
Show[mr1, HighlightMesh[mr2, 1], 
 ListLinePlot[First@First@MeshPrimitives[mr2, 2], 
  PlotStyle -> Directive[Thick, Red]]]

And, applied to the OP,

ListLinePlot@First@First@MeshPrimitives[#, 2] &@
 BoundaryDiscretizeRegion@alphaShapes2DC[pts, 5.5]

Let's look at a simpler example to show the problem. We'll create a Delaunay mesh from some random points, and generate a RegionBoundary from that.

In version 10.4:

SeedRandom[4];
mr1 = DelaunayMesh[RandomReal[1, {15, 2}]];
mr2 = RegionBoundary[mr1];
Show[mr1, HighlightMesh[mr2, 1], 
 ListLinePlot[MeshCoordinates@mr2, 
  PlotStyle -> Directive[Thick, Red]]]

compared with version 10.3.1 (or any previous version 10.x)

Let's look at the InputForm for this in 10.4,

mr2 // InputForm


MeshRegion[{.....}, {Line[{{2, 6}, {1, 2}, {4, 1}, {3, 5}, {6, 3}, {5, 4}}]}]

versus for 10.3,

MeshRegion[{.....}, {Line[{{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6,1}}]}]

How to get around this? Create a BoundaryMeshRegion and extract the polygon points from that (the points of a polygon must be in the right order or it's nonsense). The following gives identical results in 10.3 and 10.4

SeedRandom[4];
mr1 = DelaunayMesh[RandomReal[1, {15, 2}]];
mr2 = BoundaryDiscretizeRegion[mr1];
Show[mr1, HighlightMesh[mr2, 1], 
 ListLinePlot[First@First@MeshPrimitives[mr2, 2], 
  PlotStyle -> Directive[Thick, Red]]]

And, applied to the OP,

ListLinePlot@First@First@MeshPrimitives[#, 2] &@
 BoundaryDiscretizeRegion@alphaShapes2DC[pts, 5.5]