It's unlikely, but plausible
The accepted answer from the question you linked argues that bipedalism is something you can realistically expect from a large portion of intelligent species in the universe. So it's already looking good.
As long as the alien "human" planet has a similar climate and general geography, it wouldn't be surprising for them to have similar general outward traits, such as skin and perhaps even hair in all the same places of similar frequency. Placement of eyes, nose, and ears could very well be the same, though ear shapes and dental layout could vary quite easily. It wouldn't be absurd to see melanin in an alien species, so hair colors being in the same range is reasonable.
There is some room for variance in digit count, but not enough to raise any plausibility concerns regarding having 10 fingers and 10 toes. Finger and toe nails? It's just a re-purposing of claws, which probably exist in a significant portion of land dwellers on nearly any life-supporting planet.
A near-human alien wouldn't necessarily need to be a mammal or have the same expression of sexual dimorphism: A female-equivalent in this species might not have breasts or broad hips, or males may be just as naturally muscular (or less) as females. Males might be the ones to carry offspring. They might lay eggs instead of having live births. There might not even be biological sex or dimorphism at all. There are a lot of possibilities here.
Internal organs will likely be different in shape and/or placement, but blood will almost certainly still be red and carry oxygen; bones will be made of calcium and filled with marrow; and digestive tracts will flow from top to bottom.
DNA layout isn't going to match, but that only really matters for cross-breeding.
Basically, from most variable to least variable, probably disputable by someone with a stronger biology background:
- DNA layout
- Internal organ shapes and layout
- Blood compatibility (transfusions are extremely unlikely to work)
- Presence/absence of minor organs such as the pancreas, spleen, tonsils, or appendix.
- Ear shape
- Dental layout
- Sexual dimorphism
- Hair layout
- Ear placement
- Pool of available pigments for hair/eyes/skin (only a partial overlap is needed here, though melanin or another brown pigment is a must)
- General skeletal structure, including digit count
- Number of chambers in heart
- Placement of brain
- Bone Structure
- General mechanics of blood, heart, brain, and lungs
A lot of things have to align, but it's a plausible probability as long as you don't care about internal organs matching and you don't need cross-breeding for your story to work.