Short answer: Yes, the MTR by-laws are enforced by staff in the MTR by-laws enforcement team (附例執行組) and by-laws inspection unit (附例特檢隊). In most of the cases, these two units only target those whose baggage is obviously oversized or overweight, if they decided to focus on baggage rules on that day (but don't count me on that). However, if they decided to give your baggage an inspection, they could be extremely strict on the limit.

Long answer:

Who enforces the Hong Kong MTR by-laws?

All MTR by-laws are enforced by staff in either the MTR by-laws enforcement team, or the by-laws inspection unit, as confirmed by the Government's response to a Legislative Council member's question:

(d) The MTR By-law Enforcement Team and By-laws Inspection Unit would enforce the MTR By-laws.

While these officers are most seen fining those who boarded the First Class in East Rail Line without the right tickets, they do enforce a wide range of by-laws, as evident in the following job advert for a by-laws inspection lead (Chinese only), or a Customer Services and Revenue Protection Officer (note as it is a live posting, the link will be taken down soon):

Responsibilities

• Conduct ticket inspections on railway premises
• Assist passengers on the proper use of station facilities and equipment as well as the ticketing systems
• Enforce MTR by-laws and take proper actions against ticket abusers or by-laws offenders
• Assist in incidents handling and passengers in need
• Support on crowd control, set up MTR shuttle bus stops and information dissemination during service disruptions, festivals or special events
• Perform duties related to Railway Safety Rules as required

The advert for the by-laws inspection lead mentioned baggages in particular (translation mine):

防止乘客攜帶不符合公司現行規定的大型行李或危險物品進入鐵路範圍
(Prevent passengers from bringing prohibited items - non-complying large baggage or dangerous goods - into railway premises)

Do these people actually work?

Yes, according to South China Morning Post (SCMP, a broadsheet newspaper, despite the very clickbait-y title), a fair number of prosecutions are made for offending the by-laws in 2015 for bringing baggage that does not comply with the rules:

Last year, a total of 2,643 prosecutions were made against passengers for breaking the MTR’s bylaws. The second-most broken rule, after failing to pay the MTR fare, was bringing prohibited items onto the train—most of which are classified as either too large or too heavy. Bylaw 27(a) prohibits passengers from bringing luggage onto the train that could potentially cause injury to others, or cause a nuisance.

Last July, former professional snooker player Ivan Chan Kwok-ming was issued a warning letter because his cue stick was too long. Two months later, a student received a warning letter when he brought a cello onto the train. The cello was four centimeters too long.

The cello incident caused an outcry among the general public, especially MTR was seen back then not doing enough to address the parallel trading activities and the nuisance it brings to the local community, e.g. in the Northern District.

This leads to the implementation of the baggage weight limit on the East Rail Line, and the Oversized Musical Instrument Permit as photographed by the OP in the question:

Also last year, the MTR carried out a trial scheme where passengers could register for an Oversized Musical Instrument Permit. This allows musical instruments up to 145 centimeters long to be carried onto the train. (SCMP)

Do I have to worry too much?

No, unless you are doing something visibly outrageous. On the other hand, look out (and plan) for officers having a bad mood on the day.

To support this argument, let's put the numbers in perspective. As mentioned above there are ~2,000 prosecutions in a year, of which at most a half (as it is the second most popular offence) are baggage-related, that is around 1,000 a year.

This is an order less than those who have to pay a surcharge for travelling on the First Class without the right tickets, which does not lead to a prosecution if you pay up. From the Government:

From 2008 to the first quarter of 2010, a total of 22,202 passengers paid a surcharge of HK$500 in accordance with the MTR By-laws and Conditions of Issue of Tickets for failing to produce a valid ticket while travelling in First Class compartments.

This means those who enforce the by-laws tend to pick the low-hanging fruits, namely those who don't have a valid ticket for East Rail Line First Class, and hot spots for oversized baggage. Indeed, I have only seen the enforcement teams outside First Class and the adjacent platform area a couple of times during years of travelling on the system.

As a result, in practice if you are not seen (by a staff, or a concerned member of the public) carrying baggage of visibly outrageous quantities that could cause a nuisance to others, you should be fine. Of course, be warned that in the unlikely case that an by-laws enforcement officer decided to enforce that particular rule, they can go very strict as reported by the SCMP article.

@Willeke has noted that one can combine multiple baggage into one to comply with the notice:

... to travel with one piece of baggage (or smaller pieces grouped together to make one).

...so two is fine as long as you can handle them. The same can be said regarding the weight of the baggage.