I will attempt to answer the underlying question which seems to be:
Why in God's name would a country, in the year 2018, not have a
computerized entry system to enforce this stuff?
In order to have a computerized entry system - or more accurately, a digital border control enforcement, the country itself must have digitally enhanced immigration framework in place.
After all, you cannot maintain a digital database of immigration for visitors and a separate one for citizens and permanent residents.
Next, you have to look at a cost of such a system - which isn't trivial. It starts with establishing a digital identity system, enrolling everyone (including everyone in the country, and everyone outside via the embassy); next you have to issue digitized travel documents - again, non trivial.
You may have to invest in robust IT and DR/BC controls; hire security experts, do training of staff, publish and update procedures, get certified by various standards bodies.
Now you are ready to start enforcing digital border controls; starting with recording entries and exits digitally (in addition to stamping on passports), leading to e-visa (removal of the sticker based visa - a measure against fraud), and then followed by e-gate (self-service immigration controls) and finally ending up with passport less travel (you can enter on other digitally issued government ids, such as driver's licenses or id cards).
All that is a great burden on a country who is not a target of illegal immigration (many are not) and who do not have the budget to undertake such a comprehensive overhaul.
Some may have put in lax controls especially if a country relies heavily on tourism - the various penalty fees may be a significant source of ancillary revenue.