You need to use parentheses in the matching expression. This will do two things for you: make the "|" work the way you want AND give you the matched string as $1:

if ( /\b(API|APIN|UWI)\s*\./ ) { $myvar = $1 }
# $1 is set to whatever was matched inside the parens
# (if there were more than 1 set of parens, additional
# paren'ed strings would be set to $2, $3...
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As you originally wrote the expression, it would match "API" following a word boundary, or "APIN" anywhere on a line (e.g. in CHAPIN), or "UWI\s*\." anywhere on a line.

Read the perlre documentation -- it's long, but very worthwhile.