Unfortunately, it is difficult and complicated to try to access backups that were made by one Mac with another different Mac. There are no guarantees. In some cases, it is not possible.
We'll try to help, but please keep your expectations quite low.
On the MacBook Air.......
Click on the Finder "smiley face" icon on the dock at the bottom of the screen
Look on the left panel of the next window that appears for the "Locations" heading. On older Macs, the heading might read "Devices"
Does the name of the Time Capsule appear here?
If yes, click on the name of the Time Capsule and another window will open to the right with the name of the Time Capsule hard drive......(which is normally "Data" by default unless you have renamed the hard drive on the Time Capsule)
Double-click on "Data".
If Data can open, it may take some time 15-20 minute or more before the next window will appear
The next window that appears will display separate "sparsebundle" files with the name of the Mac as part of the file name.
Do you see a "sparsebundle" file with the name of the old Mac?
Post back on your progress please........but DO NOT attempt to open the sparsebundle file at this time, as it is very easy to make a mistake, which can render the backups unusable. The things that we mention are NOT supported by Apple, so they will not be able to help in the event of problems.
If we are able to proceed, please understand that it will be at your own risk.