There are a number of ways of doing this.
The first one that comes to mind is via LOOKUP:
Assuming your values are in column C:
=LOOKUP(C2,{"Bird","Cat","Dog","None"},{1,2,3,0})
Note that the list is disconnected - that is, if you add/remove options to/from the popup menu you'll need to manually adjust the formula to account for it.
The number of keywords and scores must match, so there's one value for each key, otherwise it'll throw an error.
It's also possible to do this via a sub-table where you have a mini-list of the keywords and scores, like:

using a LOOKUP() to find the matching score:
=LOOKUP(C2,Table 3::A,Table 3::B)
which reads as 'look in Table 3::A to find the value in C2, then return the corresponding value from Table 3::B.
The subtable can be hidden or located on another sheet to keep it out of the way, and this makes it easier to adjust the list/scores (you will still need to manually keep it in synch with changes to the popup menu options)