Is starch and glycogen digestion intra or extracellular?
The problem with your question is that, right now, you have three different questions:


Is the starch/glycogen digestion intra or extracellular?
Do humans have the enzyme for intracellular digestion of starch?
Do plants have the ability to digest glycogen?


Unfortunately, that goes against Bio SE rules: you have to pick one question, otherwise your post will be closed as too broad ("Avoid asking multiple distinct questions at once.").

That being said, I'll address only this question:


  Do humans have the enzyme for intracellular digestion of starch?


The answer is yes. Intracellular digestion in humans (as in any animal) is performed by lysosomes, organelles that contain hydrolytic enzymes.

Lysosomes can digest proteins, lipids, carbohydrates, nucleic acids etc. Regarding digestion of carbohydrates, this is a short list of enzymes (the complete list is way bigger) found in human lysosomes:


alpha-Galactosidase  
alpha-L-Fucosidase beta-Galactosidase-1
beta-Glucuronidase Chitinase  
Chondroitin B Lyase/Chondroitinase B
Chondroitinase 
Cytosolic beta-Glucosidase 
Galactosylceramidase
Heparanase 
Hyaluronidase 
Lysosomal alpha-Glucosidase 
O-GlcNAcase
O-Glycosidase


Among the enzymes listed above, this is the one that answers your question:
 Lysosomal alpha-Glucosidase. 

That enzyme, which is a α-1,4-glucosidase, breaks down starch (and glycogen) to glucose.

Source:


Lübke, T., Lobel, P. and Sleat, D. (2009). Proteomics of the lysosome. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 1793(4), pp.625-635..