I am happy to help.

WordCharacter represents a single word character. So the string pattern

WordCharacter..

represents a sequence of one or more word characters. So your StringCount computation,

StringCount["Hello my name is Kyle",WordCharacter..]

is returning the "lumps" that correspond to full self-contained groups of word characters. This is what StringCount is designed to do.

?StringCount

StringCount["string","sub"] gives a count of the number of times "sub" appears as a substring of "string". 
StringCount["string",patt] gives the number of substrings in "string" that match the general string expression patt. 
StringCount["string",{Subscript[patt, 1],Subscript[patt, 2],\[Ellipsis]}] counts the number of occurrences of any of the Subscript[patt, i]. 
StringCount[{Subscript[s, 1],Subscript[s, 2],\[Ellipsis]},p] gives the list of results for each of the Subscript[s, i].  >>

For fun compare your example with

StringCount["Hel8lo my name is Dav7id", LetterCharacter ..]

I think that the actual specification for WordCharacter (as well as LetterCharacter) applies only to the characters in the 256 length ASCII set. If you stick to that interpretation (and assume that the documentation is in error) then you will be fine.

Actually I am a bit confused by this. The documentation says

WordCharacter matches any character for which either LetterQ or DigitQ yields True. 

So this

In[1]:= LetterQ /@ CharacterRange["\[Alpha]", "\[Omega]"]

Out[1]= {True, True, True, True, True, True, True, True, True, True, \
True, True, True, True, True, True, True, True, True, True, True, \
True, True, True, True}

would suggest that all lowercase greek characters are WordCharacters.

However we have this:

In[2]:= StringMatchQ[#, WordCharacter] & /@CharacterRange["\[Alpha]", "\[Omega]"]

Out[2]= {False, False, False, False, False, False, False, False, \
False, False, False, False, False, False, False, False, False, False, \
False, False, False, False, False, False, False}

So this clearly is not consistent with the statement in the documentation....

Any expert care to comment?

It is one of the letters a through z (upper or lower case) or one of the integer digits 0 through 9,

In[1]:= CharacterRange[" ", "~"]

Out[1]= {" ", "!", "\"", "#", "$", "%", "&", "'", "(", ")", "*", "+", ",", "-", ".", \
"/", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", ":", ";", "<", "=", \
">", "?", "@", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", \
"M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z", "[", \
"\\", "]", "^", "_", "`", "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", \
"k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", \
"z", "{", "|", "}", "~"}

Those of these which match WordCharacter:

In[2]:= Select[CharacterRange[" ", "~"], StringMatchQ[#, WordCharacter] &]

Out[2]= {"0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", \
"F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", \
"U", "V", "W", "X", "Y", "Z", "a", "b", "c", "d", "e", "f", "g", "h", "i", \
"j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", \
"y", "z"}

Greek characters are not part of this:

In[3]:= Select[CharacterRange["\[CapitalAlpha]", "\[CapitalOmega]"], 
 StringMatchQ[#, WordCharacter] &]

Out[3]= {}